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12.1

12.1. Trigonometric Functions in Right Triangles. Recall from Geometry :. Pythagorean Theorem: a 2 + b 2= c 2 SOH CAH TOA Sin= Cos = Tan=. Hypotenuse. Opposite. Angle. Adjacent. There are 3 more trig functions to know. Example 1.

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12.1

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  1. 12.1 Trigonometric Functions in Right Triangles

  2. Recall from Geometry: Pythagorean Theorem: a2+b2=c2 SOH CAH TOA Sin= Cos = Tan= Hypotenuse Opposite Angle Adjacent

  3. There are 3 more trig functions to know

  4. Example 1 A) Find the values of the six trigonometric functions for angle G.

  5. Example 1 B) Find the values of the six trigonometric functions for angle θ.

  6. Example 2 In a right triangle, A is acute and . Find the value of csc A.

  7. Example 3 In a right triangle, Bis acute and . Find the value of sec B.

  8. Find a missing side Example 4: Find the length of y.

  9. Example 5 Find the length of x.

  10. Example 6 A) Find the measure of A. Round to the nearest tenth if necessary. A) Find the measure of B. Round to the nearest tenth if necessary.

  11. Example 7 Find the measure of A.

  12. Example 8 Solve ∆ABC when C is a right angle and a = 6, c = 14. **Notice that angles are capital letters, and the sides opposite these angles are the same letter, but lowercase. This is NOT a coincidence!!

  13. Example 9 Mario hits a line drive home run from 3 feet in the air to a height of 125 feet, where it strikes a billboard in the outfield. If the angle of elevation of the hit was 22°, how far in the air did it travel?

  14. Example 10 The hill of the roller coaster has an angle of descent, or an angle of depression, of 60°. Its vertical drop is 195 feet. From a blimp, the apparent distance traveled by the roller coaster is the horizontal distance from the top of the hill to the bottom. Find the horizontal distance.

  15. Example 11 To calculate the height of a tree in his front yard, Anand walked 50 feet from the base of the tree and used an inclinometer to measure the angle from his eye to the top of the tree, which was 62°. If Anand’s eye level is at 6 feet, about how tall is the tree?

  16. Example 12 At a certain time of the day a person six feet tall casts a four foot long shadow. Approximate the angle of elevation of the sun.

  17. 10 6 8 A C B Warm up 1. Find the value of 2. Solve ∆PQR given that cosθand cot θ. Q is a right angle, P = 33o and r = 8.

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