1. CHAPTER 8 RIGHT TRIANGLES
8-5
TRIGONOMETRY
THE TANGENT RATIO

2. TRIGONOMETRY
Trigonometry is a branch of math that deals with side-angle relationships of triangles.
In this and the following sections, we will study right triangle trigonometry.

3. TRIGONOMETRY
When applying trigonometry to right triangles, it is important that we understand the following terms:
Hypotenuse
Opposite Leg A
Adjacent Leg

4. THE TANGENT RATIO
The tangent ratio involves the opposite and adjacent sides of a triangle from a given acute angle.
*Tangent of A = leg opposite A / leg adjacent A
Hypotenuse
Opposite Leg A
Adjacent Leg

5. EXAMPLE
Find tan A & tan B. Express answers as ratios. 7 A C 2 B

6. EXAMPLE
Find tan m A and m B A 17 B 8 C

7. GRADE OF A ROAD
The grade of a road is a ratio of its rise to its run and is given as a decimal or percent.
The grade of a road is its tangent ratio expressed as a percent.
grade
Rise
(Opp.)
Run
(Adj.)

8. EXAMPLE
The grade of a road is 7%. What angle does the road make with the horizontal?
4 degrees

9. PRACTICE Find x to the nearest tenth.10 10 7
78.2
35° x x 30
21° x

10. PRACTICE Find y° correct to the nearest degree.8 58 37 5 y° 8 6 y° 10

11. CLASSWORK/HOMEWORK 8.5 Assignment
Pgs , Classroom Exercises 1-11
Pgs , Written Exercises 1-20 all