Topic Name Homework Sheet 123 Name: ______

Maths Quest 11 Maths B for Queensland Chapter 4 Triangle Trigonometry WorkSHEET 4.2 1

WorkSHEET 4.2 Triangle Trigonometry Name: ______

1 Find the unknown marked sides correct to 2 10 4 tan 37° = decimal places. x 10  x = tan37 x = 1327 (correct to 2 decimal places) 10 sin 37° = h 10  h = sin 37 h = 16.62 (correct to 2 decimal places)

2 Find the value of . 10 2 tan  8 tan  1.25   51.3°

3 From a vertical fire tower 50 m high, the angle 3 of depression is 4° to a fire. How far away is the fire to the nearest metre is the fire?

50 tan 4°  d 50  h  tan 4° h  715 m (to the nearest metre)

4 A person 1.6 m tall stands 30 m from a building 3 and measures the angle of elevation to the top of the building as 48°. How high is the building to the nearest metre?

h tan 48° = 30  h = 30  tan 48° Maths Quest 11 Maths B for Queensland Chapter 4 Triangle Trigonometry WorkSHEET 4.2 2

h = 333 m Height of building = 33.3  1.6 m = 34.9 = 35 m (to the nearest metre)

5 In triangle ABC, a = 8, c = 12, and C = 52°. 3 Find A.

sin A sin 52°  8 12 8  sin 52° sin A  12 sin A  0.5253 A  31.7°

6 Find the value of length x correct to 1 decimal x 8 3  place. sin 57° sin 62° 8  sin 57°  x  sin 62° x  7.6 (correct to 1 decimal place)

7 Consider the figure drawn below. (a) ADB  40° a b  sin A sin B BD 50  sin 20° sin 40°

50 sin 20° BD  sin 40°

(a) Find an expression for the length BD. opp (b) sin   hyp (b) Find h correct to 1 decimal place. h sin 60°  BD h  BD sin 60° 50 sin 20° sin 60°  sin 40°  23.0 Maths Quest 11 Maths B for Queensland Chapter 4 Triangle Trigonometry WorkSHEET 4.2 3

8 Find the third side of the triangle ABC, given b2 = 82  122  (2  8  12  cos 75°) 3 a = 8, c = 12 and B = 75°. State your answer = 64  144  49.69 correct to 2 decimal places. = 158.31 b = 158.31 = 12.58 (correct to 2 decimal places)

9 Find the smallest angle in the triangle with 82  102  52 3 sides 5, 8 and 10. cos  2  8 10 139 cos  160 cos  0.8688   29.7°

10 A triangle has sides 6 cm, 7 cm and Largest side lies opposite the largest angle. 9 cm. Find the size of the largest angle correct to the nearest minute. b2  c2  a 2 cos A  2bc 62  72  92 cos  2  6  7 36  49  81  84 4  84  4    cos1   84   87°16