1. Obj: Use tangent to find the length of a side of a right triangle
10.1: Tangent Ratios
Obj: Use tangent to find the length of a side of a right triangle

2. Trigonometric Ratios
A ratio of the lengths of 2 sides of a right triangle.

3. Given an acute angle in a right triangle the 3 sides can be labeled as follows:
Leg Opposite
Leg Adjacent
Hypotenuse

4. Example a) the leg opposite b) the leg adjacent c) the hypotenuse
1) If using <B state:
a) the leg opposite
b) the leg adjacent
c) the hypotenuse
2) If using <C state:

5. Supplies:
Lined Paper
Ruler
Protractor

9. Tangent Ratio For any acute angle A of a right triangle:
Tan A= leg opposite <A = a
leg adjacent to <A b

10. Example
Find tan S and tan R as fractions in simplified form and as a decimal rounded to 4 decimal places. S
T √ R

11. Using a calculator for Tangent

12. Example
Approximate the following to 4 decimal places
1) 74
2) 35

13. Using tangent ratio to Find Leg Length
Use a tangent ratio to find the value of x. Round answer to the nearest tenth.
1) 2)

14. Indirect Measurement
FORESTRY You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of a tree. You measure the angle of elevation from a point on the ground to the top of the tree to be 59°. To estimate the height of the tree, you can write a trigonometric ratio that involves the height h and the known length of 45 feet.

15. A person travels 152 feet on the escalator stairs.
Estimating a Distance
ESCALATORS The escalator at the Wilshire/Vermont Metro Rail Station in Los Angeles rises 76 feet at a 30° angle. To find the distance d a person travels on the escalator stairs, you can write a trigonometric ratio that involves the hypotenuse and the known leg length of 76 feet.
sin 30° =
opposite
hypotenuse
Write ratio for sine of 30°.
sin 30° =
opposite
hypotenuse 76 d
Substitute.
30°
76 ft d
d sin 30° = 76
Multiply each side by d.
d = 76
sin 30°
Divide each side by sin 30°.
d = 76
0.5
Substitute 0.5 for sin 30°.
d = 152
Simplify.
A person travels 152 feet on the escalator stairs.