(A) Draw a Diagram to Show This Information

1. The height of a vertical cliff is 450 m. The angle of elevation from a ship to the top of the cliff is 23°. The ship is x metres from the bottom of the cliff.

(a) Draw a diagram to show this information.

Diagram:

(b) Calculate the value of x.

Working:

Answer: (b) ………………………………………….. (Total 4 marks)

1 2. The diagram shows a water tower standing on horizontal ground. The height of the tower is 26.5 m.

From a point A on the ground the angle of elevation to the top of the tower is 28°.

(a) On the diagram, show and label the angle of elevation, 28°.

(b) Calculate, correct to the nearest metre, the distance x m.

Working:

Answers:

(b) …………………………………………..

(Total 4 marks)

2 3. The following diagram shows a carton in the shape of a cube 8 cm long on each side:

D A F G

(a) The longest rod that will fit on the bottom of the carton would go from E to G. Find the length l of this rod.

(b) Find the length L of the longest rod that would fit inside the carton.

Working:

Answers:

(a) ………………………………………….. (b) …………………………………………..

(Total 4 marks)

4. A rectangular block of wood with face ABCD leans against a vertical wall, as shown in the BAˆ E diagram below. AB = 8 cm, BC = 5 cm and angle = 28°.

C F Wall

E 28º Ground A

3 Find the vertical height of C above the ground.

Working:

Answer: ...... (Total 4 marks)

5. ABCD is a trapezium with AB = CD and [BC] parallel to [AD]. AD = 22 cm, BC = 12 cm, AB = 13 cm.

Diagram not to scale

(a) Show that AE = 5 cm. (2)

(b) Calculate the height BE of the trapezium. (2)

4 (c) Calculate

BAˆ E; (i)

BCˆ D. (ii) (3)

(d) Calculate the length of the diagonal [CA]. (3) (Total 10 marks)

6. The diagram shows a cuboid 22.5 cm by 40 cm by 30 cm.

E F 40 cm

D C 30 cm A B 22.5 cm

(a) Calculate the length of [AC].

5 GAˆ C (b) Calculate the size of .

Working:

Answers:

(a) ...... (b) ...... (Total 4 marks)

7. In the diagram below, PQRS is the square base of a solid right pyramid with vertex V. The sides of the square are 8 cm, and the height VG is 12 cm. M is the midpoint of [QR].

VG = 12 cm

P Q 8 cm G M

S 8 cm R

(a) (i) Write down the length of [GM].

(ii) Calculate the length of [VM]. (2)

6 (b) Find

(i) the total surface area of the pyramid;

(ii) the angle between the face VQR and the base of the pyramid. (4) (Total 6 marks)

8. Andrew is at point A in a park. A deer is 3 km directly north of Andrew, at point D. Brian is 1.8 km due west of Andrew, at point B.

(a) Draw a diagram to represent this information.

(b) Calculate the distance between Brian and the deer.

(c) Brian looks at Andrew, and then turns through an angle θ to look at the deer. Calculate the value of θ.

Diagram: (a)

7 Working:

Answers:

(b) …..….……………………… (c) ……………………………... (Total 8 marks)

9. Three right pyramids Andal, Batsu and Cartos were discovered in the dense jungle of Marhartmasol. Each pyramid has a square base with centres A, B and C respectively.

Cartos A

8 A surveying team was lowered from a helicopter to the top of Andal to take measurements of the area. Andal is 40 metres high. The angle of elevation from the top of Andal to the top of Batsu is 3°. The horizontal distance from A, the centre of the base of Andal, to B, the centre of the base of Batsu is 600 metres.

(a) Use the diagram below to find the height of Batsu. (3)

40 m Andal Batsu

A B 600 m

(b) Cartos is found to be 92 metres high and the angle of elevation from the top of Andal to the top of Cartos is 4°.

(i) Draw a diagram similar to the diagram in part (a) to show the relationship between Andal and Cartos.

(ii) What is the horizontal distance from A to C? (4)

9 (c) The diagram below represents measurements relative to the centres of the bases of the pyramids. The surveyors determined the angle at A to be 110°, and the distance AB to be 600 m.

A 110º

(i) What is the distance between B and C? Give your answer to the nearest metre.

(ii) What is the size of angle ACB?

(iii) What is the area of the land inside triangle ABC? (8) (Total 15 marks)

10. The following diagram shows the rectangular prism ABCDEFGH. The length is 5 cm, the width is 1 cm, and the height is 4 cm.

A F Diagram not to scale

10 (a) Find the length of [DF].

(b) Find the length of [CF].

Working:

Answers:

(a) ...... (b) ……………………………………......

(Total 8 marks)

11. The diagram below represents a stopwatch. This is a circle, centre O, inside a square of side 6 cm, also with centre O. The stopwatch has a minutes hand and a seconds hand. The seconds hand, with end point T, is shown in the diagram, and has a radius of 2 cm.

D B T 6 cm O p q C r

(a) When T is at the point A, the shortest distance from T to the base of the square is p. Calculate the value of p. (2)

11 (b) In 10 seconds, T moves from point A to point B. When T is at the point B, the shortest distance from T to the base of the square is q. Calculate

(i) the size of angle AOB;

(ii) the distance OD;

(iii) the value of q. (5)

(c) In another 10 seconds, T moves from point B to point C. When T is at the point C, the shortest distance from T to the base of the square is r. Calculate the value of r. (4)

Let d be the shortest distance from T to the base of the square, when the seconds hand has moved through an angle . The following table gives values of d and .

Angle 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330 360°  Distance p 4.7 q 3 r 1.3 1 1.3 r 3 q 4.7 p d

12 The graph representing this information is as follows.

0º 30º 60º 90º 120º 150º 180º 210º 240º 270º 300º 330º 360º angle

The equation of this graph can be written in the form d = c + k cos().

(d) Find the values of c and k. (4) (Total 15 marks)

12. The figure below shows a hexagon with sides all of length 4 cm and with centre at O. The interior angles of the hexagon are all equal.

The interior angles of a polygon with n equal sides and n equal angles (regular polygon) add up to (n – 2) × 180°.

Bˆ (a) Calculate the size of angle A C.

(b) Given that OB = OC, find the area of the triangle OBC.

(c) Find the area of the whole hexagon.

Working:

Answers:

(a) ...... (b) ...... (c) ......

(Total 8 marks)

13. A recreation park has two trains. Train 1 takes visitors from the entrance (E) to the swimming pool (S), to the mini golf (M) and back to the entrance. Train 2 takes visitors from the entrance (E) to the play area (P), to the racing track (R) and back to the entrance. This is shown in the diagram.

E S ES = 500 m 115° SM = 400 m ER = 750 m ESM = 115° 400 m ERP = 50°

2 EPR = 90°

I 0 A 5 [not to scale] R 7

50° R

(a) Calculate the total distance Train 2 travels in one journey from E to P to R to E. (5)

(b) (i) Show that EM = 761 m correct to 3 s.f..

14 (ii) If the trains travel at 2 ms–1 find the time taken for Train 1 to complete a journey from E to S to M to E. Give your answer to the nearest second. (6) (Total 11 marks)

14. In the diagram below ABEF, ABCD and CDFE are all rectangles. AD = 12 cm, DC = 20 cm and DF = 5 cm. M is the midpoint of EF and N is the midpoint of CD.

5 cm A 12 cm D

(a) Calculate (i) the length of AF;

(ii) the length of AM. (3)

(b) Calculate the angle between AM and the face ABCD. (3) (Total 6 marks)

15 15. The following diagram shows a sloping roof. The surface ABCD is a rectangle. The angle ADE is 55°. The vertical height, AF, of the roof is 3 m and the length DC is 7 m.

7 m 3 m

55° E F D

(a) Calculate AD.

(b) Calculate the length of the diagonal DB.

Working:

Answers:

(a) ...... (b) ...... (Total 8 marks)

16 16. OABCD is a square based pyramid of side 4 cm as shown in the diagram. The vertex D is 3 cm directly above X, the centre of square OABC. M is the midpoint of AB.

(a) Find the length of XM.

(b) Calculate the length of DM.

(c) Calculate the angle between the face ABD and the base OABC.

D Diagram not to scale

Working:

Answers:

(a) ...... (b) ...... (c) ......

(Total 8 marks)

17 17. A cross-country running course is given in the diagram below. Runners start and finish at point O.

O Not to scale

110° B 800 m A

(a) Show that the distance CA is 943 m correct to 3 s.f. (2)

(b) Show that angle BCA is 58.0° correct to 3 s.f. (2)

(c) (i) Calculate the angle CAO.

(ii) Calculate the distance CO. (5)

(d) Calculate the area enclosed by the course OABC. (4)

18 (e) Gonzales runs at a speed of 4 m s–1. Calculate the time, in minutes, taken for him to complete the course. (3) (Total 16 marks)

18. The diagram shows a point P, 12.3 m from the base of a building of height h m. The angle measured to the top of the building from point P is 63°.

P 63° 12.3

(a) Calculate the height h of the building.

Consider the formula h = 4.9t2, where h is the height of the building and t is the time in seconds to fall to the ground from the top of the building.

(b) Calculate how long it would take for a stone to fall from the top of the building to the ground.

Working:

Answers:

(a) ...... (b) ......

(Total 6 marks)

19 19. A child’s toy is made by combining a hemisphere of radius 3 cm and a right circular cone of slant height l as shown on the diagram below.

diagram not to scale

(a) Show that the volume of the hemisphere is 18 cm3. (2)

The volume of the cone is two-thirds that of the hemisphere.

(b) Show that the vertical height of the cone is 4 cm. (4)

(c) Calculate the slant height of the cone. (2)

(d) Calculate the angle between the slanting side of the cone and the flat surface of the hemisphere. (3)

(e) The toy is made of wood of density 0.6 g per cm3. Calculate the weight of the toy. (3)

(f) Calculate the total surface area of the toy. (5) (Total 19 marks)

20 20. Find the volume of the following prism.

Diagram not to scale 8 cm

42° 5.7 cm

(Total 4 marks)

4.5 cm

3 cm 25°

B 3 cm C

ABˆ C ACˆ D In the diagram, AB = BC = 3 cm, DC = 4.5 cm, angle = 90 and angle = 25.

(a) Calculate the length of AC.

(b) Calculate the area of triangle ACD.

(c) Calculate the area of quadrilateral ABCD.

21 Working:

Answers:

(a) ...... (b) ...... (c) ......

(Total 8 marks)

22. Points P(0,–4), Q (0, 16) are shown on the diagram.

0 2 4 6 8 10 12 14 16 18 x

22 (a) Plot the point R (11,16).

QPˆR. (b) Calculate angle

M is a point on the line PR. M is 9 units from P.

(c) Calculate the area of triangle PQM.

Working:

Answers:

(b) ...... (c) ......

(Total 6 marks)

23 23. The figure below shows a rectangular prism with some side lengths and diagonal lengths marked. AC = 10 cm, CH = 10 cm, EH = 8cm, AE 8 cm.

8 cm E H (not to scale) 8 cm

A D 10 cm F 10 cm G

(a) Calculate the length of AH. (2)

ACˆ H. (b) Find the size of angle (3)

(c) Show that the total surface area of the rectangular prism is 320 cm2. (3)

(d) A triangular prism is enclosed within the planes ABCD, CGHD and ABGH. Calculate the volume of this prism. (3) (Total 11 marks)

24 24. The diagram below shows a child’s toy which is made up of a circular hoop, centre O, radius 7 cm. The hoop is suspended in a horizontal plane by three equal strings XA, XB, and XC. Each string is of length 25 cm. The points A, B and C are equally spaced round the circumference of the hoop and X is vertically above the point O.

B 7 cm C diagram not to scale

(a) Calculate the length of XO. (2)

(b) Find the angle, in degrees, between any string and the horizontal plane. (2)

AOˆ B. (c) Write down the size of angle (1)

(d) Calculate the length of AB. (3)

(e) Find the angle between strings XA and XB. (3) (Total 11 marks)

25 25. An old tower (BT) leans at 10 away from the vertical (represented by line TG).

MBˆ T The base of the tower is at B so that = 100.

Leonardo stands at L on flat ground 120 m away from B in the direction of the lean.

BLˆ T He measures the angle between the ground and the top of the tower T to be = 26.5.

not to scale

100° 90° 26.5° M L MB = 200 B G BL = 120

BTˆ L (a) (i) Find the value of angle .

(ii) Use triangle BTL to calculate the sloping distance BT from the base, B to the top, T of the tower. (5)

(b) Calculate the vertical height TG of the top of the tower. (2)

(c) Leonardo now walks to point M, a distance 200 m from B on the opposite side of the tower. Calculate the distance from M to the top of the tower at T. (3) (Total 10 marks)

26 26. ABCDV is a solid glass pyramid. The base of the pyramid is a square of side 3.2 cm. The vertical height is 2.8 cm. The vertex V is directly above the centre O of the base.

(a) Calculate the volume of the pyramid. (2)

(b) The glass weighs 9.3 grams per cm3. Calculate the weight of the pyramid. (2)

(c) Show that the length of the sloping edge VC of the pyramid is 3.6 cm. (4)

BVˆ C (d) Calculate the angle at the vertex, . (3)

(e) Calculate the total surface area of the pyramid. (4) (Total 15 marks)

27 ABˆ C ACˆ B 27. Triangle ABC is drawn such that angle is 90, angle is 60 and AB is 7.3 cm.

(a) (i) Sketch a diagram to illustrate this information. Label the points A, B, C. Show the angles 90, 60 and the length 7.3 cm on your diagram.

(ii) Find the length of BC. (3)

CDˆ B Point D is on the straight line AC extended and is such that angle is 20.

(b) (i) Show the point D and the angle 20 on your diagram.

CBˆ D (ii) Find the size of angle . (3)

28 Working:

Answers:

(a) (ii)...... (b) (ii)......

(Total 6 marks)

29 28. The triangular faces of a square based pyramid, ABCDE, are all inclined at 70 to the base. The edges of the base ABCD are all 10 cm and M is the centre. G is the mid-point of CD.

(Diagram not to scale)

C M A G

(a) Using the letters on the diagram draw a triangle showing the position of a 70 angle. (1)

(b) Show that the height of the pyramid is 13.7 cm, to 3 significant figures. (2)

(c) Calculate

(i) the length of EG;

DEˆ C (ii) the size of angle . (4)

(d) Find the total surface area of the pyramid. (2)

(e) Find the volume of the pyramid. (2) (Total 11 marks)

30 29. Sylvia is making a square-based pyramid. Each triangle has a base of length 12 cm and a height of 10 cm.

(not to scale)

(a) Show that the height of the pyramid is 8 cm. (2)

M is the midpoint of the base of one of the triangles and O is the apex of the pyramid.

(b) Find the angle that the line MO makes with the base of the pyramid. (3)

(c) Calculate the volume of the pyramid. (2)

(d) Daniel wants to make a rectangular prism with the same volume as that of Sylvia’s pyramid. The base of his prism is to be a square of side 10 cm. Calculate the height of the prism. (2) (Total 9 marks)

31 30. An office tower is in the shape of a cuboid with a square base. The roof of the tower is in the shape of a square based right pyramid.

The diagram shows the tower and its roof with dimensions indicated. The diagram is not drawn to scale.

O 10 m H G

A6 m B

(a) Calculate, correct to three significant figures,

(i) the size of the angle between OF and FG; (3)

(ii) the shortest distance from O to FG; (2)

(iii) the total surface area of the four triangular sections of the roof; (3)

(iv) the size of the angle between the slant height of the roof and the plane EFGH; (2)

(v) the height of the tower from the base to O. (2)

32 A parrot’s nest is perched at a point, P, on the edge, BF, of the tower. A person at the point A, outside the building, measures the angle of elevation to point P to be 79°.

(b) Find, correct to three significant figures, the height of the nest from the base of the tower. (2) (Total 14 marks)

31. A cylinder is cut from a solid wooden sphere of radius 8 cm as shown in the diagram. The height of the cylinder is 2h cm.

(a) Find AE (the radius of the cylinder), in terms of h. (2)

(b) Show that the volume (V) of the cylinder may be written as

V= 2h (64 – h2) cm3. (2)

(c) (i) Determine, correct to three significant figures, the height of the cylinder with the greatest volume that can be produced in this way. (5)

(ii) Calculate this greatest volume, giving your answer correct to the nearest cm3. (3) (Total 12 marks)

33 32. A closed box has a square base of side x and height h.

(a) Write down an expression for the volume, V, of the box. (1)

(b) Write down an expression for the total surface area, A, of the box. (1)

The volume of the box is 1000 cm3

(c) Express h in terms of x. (2)

(d) Hence show that A = 4000x–l + 2x2. (2)

dA dx (e) Find . (2)

(f) Calculate the value of x that gives a minimum surface area. (4)

(g) Find the surface area for this value of x. (3) (Total 15 marks)

34 33. Jenny has a circular cylinder with a lid. The cylinder has height 39 cm and diameter 65 mm.

(a) Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places. (3)

The cylinder is used for storing tennis balls. Each ball has a radius of 3.25 cm.

(b) Calculate how many balls Jenny can fit in the cylinder if it is filled to the top. (1)

(c) (i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on. Calculate the volume of air inside the cylinder in the spaces between the tennis balls.

(ii) Convert your answer to (c) (i) into cubic metres. (4) (Total 8 marks)

35 34. In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and angle ACB is 23°.

23º C B 15 cm

(a) the size of angle CAB;

(b) the length of AB.

Working:

Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 4 marks)

36 35. The diagram shows the plan of a playground with dimensions as shown.

48 m 117º B 57 m A

Calculate

(a) the length BC;

(b) the area of triangle ABC.

Working:

Answers: (a) ………………………………………….. (b) ………………………………………….. (Total 4 marks)

37 36. The line L shown on the set of axes below has equation 3x + 4y = 24. L cuts the x-axis at A 1 1 and cuts the y-axis at B. Diagram not drawn to scale y

x O A C

(a) Write down the coordinates of A and B. (2)

M is the midpoint of the line segment [AB].

(b) Write down the coordinates of M. (2)

The line L passes through the point M and the point C (0, –2). 2

(c) Write down the equation of L . 2 (2)

(d) Find the length of

(i) MC; (2)

(ii) AC. (2)

38 (e) The length of AM is 5. Find

(i) the size of angle CMA; (3)

(ii) the area of the triangle with vertices C, M and A. (2) (Total 15 marks)

37. The diagram below shows an equilateral triangle ABC, with each side 3 cm long. The side [BC] is extended to D so that CD = 4 cm.

B C 4 cm D

Calculate, correct to two decimal places, the length of [AD].

Working:

Answer:

...... ………………………………………….. (Total 4 marks)

39 38. A gardener pegs out a rope, 19 metres long, to form a triangular flower bed as shown in this diagram. Diagram not to scale

5 m 6 m

Calculate

(a) the size of the angle BAC; (3)

(b) the area of the flower bed. (2) (Total 5 marks)

BAˆ C 39. The following diagram shows a triangle ABC. AB = 8 m, AC = 14 m, BC = 18 m, and = 110°.

A 8 m 110º

B 14 m

40 Calculate

(a) the area of triangle ABC;

ACˆ B. (b) the size of angle

Working:

Answers:

(a) ...... (b) ...... (Total 4 marks)

40. The diagram below shows a crane PQR that carries a flat box W. (PQ) is vertical, and the floor (PM) is horizontal.

Diagram not to scale R

7.8 m 6.5 m

Q 102º W

11.1 m h

PQˆ R Given that PQ = 11.1m, QR = 7.8 m, =102° and RW = 6.5 m, calculate

(a) PR; (2)

41 PRˆ Q; (b) angle (2)

(c) the height, h, of W above (PM). (3) (Total 7 marks)

41. The figure shows two adjacent triangular fields ABC and ACD where AD = 30 m, CD = 80 m, Dˆ Aˆ BC = 50m. A C = 60° and B C = 30°.

D 60° C

30 m 50 m

Note: Diagram not 30° drawn to scale B A

(a) Using triangle ACD calculate the length AC.

42 Bˆ (b) Calculate the size of A C.

Working:

Answers:

(a) ...... (b) ...... (Total 8 marks)

42. Raul, in house R, is directly across the lake from Sylvia, in house S. The houses are two kilometres apart. When both Raul and Sylvia are facing due north, they see a speedboat B in the lake between the two houses. Raul in house R can see the boat at 35° east of where he is facing. Sylvia in house S can see the same boat at 65° west of where she is facing.

(a) Copy and complete the diagram below, indicating which is the 35° angle, and which is the 65° angle.

B diagram not to scale

R 2 km S

RBˆ S (b) (i) Calculate the size of .

(ii) At this moment, how far is the boat (B) from Raul's house (R)? Please give your answer to the nearest 100 metres. (5)

43 (c) Raul and Sylvia then see a sailboat on the lake at point Q, which is 2.6 km from Raul (R) RQˆ S and 3.5 km from Sylvia (S). Calculate the size of at that moment, giving your answer to the nearest degree. (4) (Total 11 marks)

43. The following diagram shows the side view of a tent. The side of the tent AC is 6 m high. The ground AB slopes upwards from the bottom of the tent at point A, at an angle of 5° from the horizontal. The tent is attached to the ground by a rope at point B, a distance of 8 m from its base.

6 m B 8 m 5° A

(a) Calculate the angle BAC.

(b) Calculate the length of the rope, BC.

(c) Calculate the angle CBA that the rope makes with the sloping ground.

Working:

Answers:

(a) ...... (b) ...... (c) ......

(Total 8 marks)

44. The diagram below shows a field ABCD with a fence BD crossing it. AB = 15m, AD = 20 m

44 BAˆ D BDˆ C and angle = 110°. BC = 22 m and angle = 30°.

A diagram not to scale 15 110° 20

B 30° D 22

(a) Calculate the length of BD. (3)

BCˆ D. (b) Calculate the size of angle (3)

One student gave the answer to (a) “correct to 1 significant figure” and used this answer to BCˆ D. calculate the size of angle

(c) Write down the length of BD correct to 1 significant figure. (1)

BCˆ D (d) Find the size of angle that the student calculated, giving your answer correct to 1 decimal place. (2)

BCˆ D. (e) Hence find the percentage error in his answer for angle (3) (Total 12 marks)

45 45. (a) A farmer wants to construct a new fence across a field. The plan is shown below. The new fence is indicated by a dotted line.

Diagram not to scale 75°

40° 410 m

Calculate the length of the fence. (5)

(b) The fence creates two sections of land. Find the area of the smaller section of land ABC, given the additional information shown below.

A B Diagram not to scale

(3) (Total 8 marks)

46 ABˆ C 46. In triangle ABC, AB = 3.9 cm, BC = 4.8 cm and angle = 82.

82° Diagram not to scale 3.9 cm 4.8 cm

(a) Calculate the length of AC. (3)

ACˆ B. (b) Calculate the size of angle (3) (Total 6 marks)

47 47. The diagram shows a circle of radius R and centre O. A triangle AOB is drawn inside the circle. The vertices of the triangle are at the centre, O, and at two points A and B on the circumference. AOˆ B Angle is 110 degrees.

R 110° R O

(a) Given that the area of the circle is 36 cm2, calculate the length of the radius R.

(b) Calculate the length AB.

(c) Write down the side length L of a square which has the same area as the given circle.

Working:

Answers:

(a) ...... (b) ...... (c) ......

(Total 6 marks)

48 48. The figure shows a triangular area in a park surrounded by the paths AB, BC and CA, where ABˆ C BCˆ A AB = 400 m, = 50 and = 30.

A diagram not to scale

30º C B

(a) Find the length of AC using the above information.

Diana goes along these three paths in the park at an average speed of 1.8 m s–1.

(b) Given that BC = 788m, calculate how many minutes she takes to walk once around the park.

Working:

Answers:

(a) ...... (b) ......

(Total 6 marks)

49 49. On a map three schools A, B and C are situated as shown in the diagram.

Schools A and B are 625 metres apart. ABˆ C Angle = 102 and BC = 986 metres.

102 A B 625 m

(a) Find the distance between A and C. (3)

BAˆ C (b) Find the size of angle . (3)

Working:

Answers:

(a) ...... (b) ......

(Total 6 marks)

50 ABˆ C ACˆ B 50. Triangle ABC is such that AC is 7 cm, angle is 65 and angle is 30.

(a) Sketch the triangle writing in the side length and angles. (1)

(b) Calculate the length of AB. (2)

(c) Find the area of triangle ABC. (3)

Working:

Answers:

(b) ...... (c) ......

(Total 6 marks)

51. Amir needs to construct an isosceles triangle ABC whose area is 100 cm2. The equal sides, AB and BC, are 20 cm long.

ABˆ C ABˆ C (a) Angle is acute. Show that the angle is 30. (2)

(b) Find the length of AC. (3) (Total 5 marks)