1. Objectives: Evaluate trigonometric functions of acute angles Solve right triangles Use trigonometric functions to model and solve real-life problems

2. The Six Trigonometric Functions Consider a right triangle with one acute angle labeled. Relative to the angle, the three sides of the triangle are the hypotenuse, the opposite side (the side opposite the angle ) and the adjacent side (the side adjacent to the angle ) hypotenuse opposite side adjacent side

3. Right Triangle definitions of Trigonometric Functions The six trig functions:

4. EX: Use the triangle to find the values of the six trig functions of both acute angles. 1. 7 24

5. EX: Use the triangle to find the values of the six trig functions of both acute angles. 2. 7 6

6. Solving Right Triangles In this type of application, you are usually given one side of a right triangle and one of the acute angles and are asked to find one of the other sides, or you are given two sides and are asked to find one of the acute angles. Angle of elevation: the angle from the horizontal upward to an object Angle of depression: the angle from the horizontal downward to an object

7. EX: Solve the right triangle 3.

8. EX: Solve the right triangle 4.

9. EX: Solve the application problem 5.A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as. How tall is the Washington Monument?

10. EX: Solve the application problem 6.A historic lighthouse is 200 yards from a bike path along the edge of a lake. A diagonal walkway to the lighthouse is 400 yards long. Find the acute angle between the bike path and the walkway (the angle of depression).

11. EX: Solve the application problem 7.Find the length of a loading ramp that is attached to a building at a height of 3.5 feet and makes an angle of with the ground. Then find the distance from the building the loading ramp is on the ground.