1. Notes # ____
12.4 Tangent Ratio

2. Vocabulary trigonometry : the study of the properties of triangles
trigonometric ratio : ratio of measures of two sides of a right triangle
tangent : in a right triangle, the ratio of the leg opposite the acute angle to the leg adjacent to the acute angle

3. Definition A C B
hypotenuse
leg adjacent to A
leg opposite A

4. Ex 1
Find tan A and tan B. A C B 41 40 9

5. Ex 2
Find tan P and tan Q. P R Q 5 4 3

6. Tangents with Angle Measurements
Ex 3
Tangents with Angle Measurements
Find the measurement of DF.
The tangent of an angle depends on the angle, not the size of the triangle. F D E
70
45 m

7. Ex 4
Find the measurement of QR. R Q P
55
20 m

8. Angles of Elevation and Depression
Find the measurement of DF.
Applications of trigonometry may include these angles
angle of depression
angle of elevation

9. Ex 5
Find the height of the tree C A
5 ft
40 B
100 ft

10. Ex 6 Find the angle of elevation.
arctangent is the same as inverse tangent C
10 ft B
48 ft A

11. Ex 7
Find the angle of depression. C
760 ft B
5000 ft A