Geometry Notes G.8 Intro to Trigonometry Mrs. Grieser Name: ______Date: ______Block: ______ How do we find an unknown side length of a right triangle if we know one side and one angle?  Trigonometry: Greek for “measurement of triangles”  Based on ratios of sides in a right triangle and how the ratios relate to angle measurement.  Trigonometric ratios are relative to an angle: we look at side lengths opposite and/or adjacent (next to) a specific angle. o The figure at right shows adjacent and opposite sides relative to A .  Three basic trigonometric ratios we will look at: o sine (sin), cosine (cos), and tangent (tan)  The table at right describes the trigonometric ratios relative to . o Find the trig ratios relative to C : sin C = _____ cos C = _____ tan C = _____

Example: Write the trigonometric ratios relative to X and Y : sin X = ______sin Y = ______cos X = ______cos Y = _____ tan X = _____ tan Y = _____

Using the TI-83 Plus calculator 1) Put in degree mode (select MODE) 2) Select trig function 3) Enter angle value 4) Force degree mode: <2nd>Angle:1

Application Examples:  Find acute angle you know  Set up trig function and solve a) Find x and y. b) Find x and y.

Geometry Notes G.8 Intro to Trigonometry Mrs. Grieser Page 2 You Try: Find the missing sides… a) b) c)

d) A right triangle has side lengths of 8, 15, and 17. Angle X is opposite to the side of length 15. Angle Y is opposite to the side of length 8. Angle Z is opposite the hypotenuse. Draw a picture, and state the following trigonometric ratios: sin X = ______sin Y = ______cos X = ______cos Y = ______tan X = ______tan Y = ______Trigonometric Values of Special Triangles sin 45o = ______cos 45o = ______tan 45o = ______

sin 30o = ______sin 60o= ______cos 30o = ______cos 60o=______tan 30o = ______tan 60o= ______

Summary:

Solve using trigonometry: 2) a) BC = 7, AB = _____ 1) a) AC = 7, BC = _____ b) AB = 14, BC = _____ b) BC = 10, AB = _____ c) AC = 9 3 , BC = ____ c) AB = 11 2 , BC = _____ d) AB = 16, AC = ____ d) AB = 10, AC = _____

Geometry Notes G.8 Intro to Trigonometry Mrs. Grieser Page 3 Angle of Elevation / Depression  Angle of elevation: angle your line of sight makes with the horizontal when you look up  Angle of depression: angle your line of sight makes with the horizontal when you look down Example: a) From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º. Find to the nearest foot, the height of the tree.

b) From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40º. How many feet, to the nearest foot, must the cat walk to reach the barn?

c) John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. How tall is the tree?

d) If the angle of depression from the top of a 40 m tall lighthouse to a ship at sea is 18o, how far is the ship from the shore to the nearest meter?

You Try: a) Find AC using trigonometry (to the nearest b) You are at the top of a roller coaster 100 feet hundredth). above the ground. The angle of depression is 44°. About how far do you ride down the hill (to the nearest foot)?