Right Triangle Trigonometry

1. Right Triangle Trigonometry Section 4.3

2. Objectives • Calculate any trigonometric function for an angle in a right triangle given two sides of the triangle. • Calculate the length of the sides of a right triangle given the measure of an angle of a triangle. • Solve word problems requiring right triangles and trigonometric functions.

3. Vocabulary • angle of elevation • angle of depression

4. Trigonometric Functions • sin(x) • cos(x) • tan(x)

5. Trigonometric Functions • csc(x) • sec(x) • cot(x)

6. For the triangle y • Find sin(x) • Find cos(y) • Find tan(x) • Find cot(y) 3 x 5

7. For the triangle y • Find sec(x) • Find csc(y) 3 x 5

8. Identities • Cofunction Identities • sin(x) = cos(90-x) • cos(x) = sin(90-x) • tan(x) = cot(90-x) • cot(x) = tan(90-x) • sec(x) = csc(90-x) • csc(x) = sec(90-x)

9. C β α B A For the triangle below, if BC = 7 and the angle β = 60, find all the missing angles and sides.

10. A plane if flying at an elevation of 27000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 25 degrees. Find the distance between the plane and the airport.

11. A hot-air balloon is floating abovea straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 23 degrees and 27 degrees. How high (in feet) is the balloon?

12. The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the Empire State Building.