1. 9.5 Trigonometric Ratios
Advanced Geometry

2. TRIGONOMETRIC RATIO
A trig ratio is a ratio of the lengths of two sides of a right triangle. There are three basic trig ratios:
sine cosine tangent
sin cos tan

3. SINE

4. COSINE

5. TANGENT

7. Find sin, cos, and tan of A

8. Example
Compare the sine, the cosine, and the tangent ratios for angle A in each triangle below.

9. Example
Find the sine, the cosine, and the tangent of angle D and angle E.

10. Use A Calculator
Use a calculator to approximate the sine, cosine, and tangent of 82 degrees.

11. Use a Calculator
Use a calculator to approximate the sine, cosine, and tangent of 54 degrees.

12. Sin and Cos must always be less than 1!!
Note:
Sin and Cos must always be less than 1!!

14. Using Trig to find lengths

15. Using Trig to find lengths

16. Using Trig to find lengths

17. ANGLE OF ELEVATION
The angle that your line of sight makes with a line drawn horizontally is called the angle of elevation.

18. Example
You are measuring the height of a building. You stand 100 feet from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 48 degrees. Estimate the height of the building.

19. Example
A driveway rises 12 feet over a distance d at an angle of 3.5 degrees. Estimate the length of the driveway.

20. Example
The angle of elevation from the base to the top of a waterslide is about 13 degrees. The slide extends horizontally about 58.2 meters. Estimate the height of the slide.

21. Example
Your family room has a sliding-glass door with a southern exposure. You want to buy an awning for the door that will be just long enough to keep the sun out when it is at its highest point in the sky. The angle of elevation of the sun at this point is 70°, and the height of the door is 8 feet. About how far should the overhang extend?