Trigonometric Functions Chapter 4

4.1 Right Triangle Trigonometry Finding the six trigonometric ratios. Solving right triangles. Using a calculator to find trig ratios.

Trigonometric Ratios: ratios of sides of a right triangle. θ hyp hyp opp adj θ adj opp Θ is an acute angle!!!!!!

6 Trigonometric Ratios: 3 basic: 3 additional:

Since any two right triangles with angle θ are similar, these ratios are the same, regardless of the size of the triangle. 50 30 5 3 θ θ 4 40

You try… Find the values of the 6 trig ratios of angle θ: 7 θ 3

If , find the other 5 trig ratios.

Solving Right Triangles: determine 3 side lengths and 3 angle measures Solving Right Triangles: determine 3 side lengths and 3 angle measures. Must give you three out of 6 parts. Angles Sides A = a = B = b = C = c = + 180° Pythag Th A c b B C a CHECK MODE OF CALCULATORS!

Solve the Right Triangle Angles Sides A = 42° a = B = b = C = c = 4 A c b B C a

Solve the Right Triangle Angles Sides A = a = 3 B = b = C = c = 14 A c b B C a

Applications: Line of sight: line from observer’s eye to object Angle of elevation: object is above horizontal, angle between line of sight and horizontal Angle of depression: object is below horizontal, angle between line

Example A person standing 100 feet from the bottom of a cliff notices a tower on top of the cliff. The angle of elevation to the top of the cliff is 30°, and the angle of elevation to the top of the tower is 58°. How tall is the tower?

Checkpoint. You are standing on top of a vertical cliff 40 meters high. You see your car parked away from the base of the cliff. The angle of depression that your car makes with the cliff is 34º.  How far is the car from the base of the cliff?

4.1 Homework p. 227 #6, 12, 18, 22, 34, 42, 56, 57 – 67 odd p. 52 #25, 35, 66, 67