1. Date: Topic: Trigonometry – Finding Side Lengths (9.6) Warm-up: A B C 4 6 SohCahToa

2. Finding Side Lengths We can use sine, cosine, and tangent to help us find missing side lengths on right triangles. 34° 13 x First, identify which trig ratio to use. hypotenuse adjacent Then, set up a proportion. Cross multiply. Use a calculator to multiply. Make sure in degree mode. Round to the nearest tenth. 10.8

3. Use sin, cos, or tan to find y. 57° y 14 opp adj Set up a proportion Divide using a calculator Make sure in degree mode Round your answer to the nearest tenth 9.1 Use which trig ratio? Divide to solve for y Cross multiply

4. A 15 foot ladder is leaning against a wall. The foot of the ladder creates a 72° angle with the ground. How far does the ladder reach up the wall? 72° 15 feet opp hyp Set up a proportion. Multiply with a calculator in degree mode Write your answer in a complete sentence: The ladder reaches 14.3 feet up the wall. 14.3 feet x Use which trig ratio? Round your answer to the nearest tenth

5. Inverse Trigonometric Ratios The inverse trigonometric ratios help us find angle measures of a right triangle when we are given side lengths. The inverse trigonometric ratios are: Inverse Sine Inverse Cosine Inverse Tangent

6. Finding Angle Measures We can use the inverses of sine, cosine, and tangent to find missing angle measures in right triangles. x° 12 15 opp adj Trig ratio Use inverse tangent to find x. Calculator in degree mode. Round answer to the nearest tenth. 38.7° Use which trig ratio?

7. Use inverse sin, cos, or tan to find y. y° 27 14 hyp adj Trig ratio Use inverse cosine, calculator in degree mode Round answer to the nearest tenth 58.8° Use which trig ratio?

8. An airplane takes off from San Diego to San Francisco. When the plane has traveled 1000 feet, it is 625 feet in the air. What is the angle between the plane’s flight path and the ground? 625 feet x° 1000 feet hyp opp Trig ratio: Solve for x: Write your answer in a complete sentence: The angle between the plane’s flight path and the ground is 38.7°. 38.7° Use which trig ratio?