2. Main Idea and New Vocabulary Key Concept: Tangent Ratio
Example 1: Find the Tangent
Example 2: Use Tangent to Find Missing Lengths
Lesson Menu

3. Use the tangent ratio to find missing measures of right triangles.
trigonometry
trigonometric ratio
tangent ratio
Main Idea/Vocabulary

4. Key Concept

5. Find the Tangent
Find tan A in the triangle shown below. Round to the nearest hundredth. Explain its meaning.
Answer: Tan A ≈ 1.33, so the side opposite A is about 1.33 times as long as the side adjacent A.
Example 1

6. Find tan B in the triangle shown below
Find tan B in the triangle shown below. Round to the nearest hundredth if necessary.
A. 0.6
B. 0.75
C. 0.8
D. 1.33
Example 1 CYP

7. Use Tangent to find Missing Lengths
BUILDINGS Sheila is looking at the top of a building at a 40° angle. If she is sitting 20 meters from the base of the building, how tall is the building?
Write the tangent ratio.
Example 2

8. Use Tangent to find Missing Lengths
Substitution
Multiply each side by 20.
ENTER ×
TAN
Use a calculator.
x  Simplify.
Answer: The building is about 16.8 meters tall.
Example 2

9. RIDES Seth is looking at the top of a roller coaster hill at a 68° angle. If he is standing 14 meters from the base of the hill, how tall is the roller coaster hill? Round to the nearest tenth.
A. 2.5 meters
B. 5.7 meters
C meters
D meters
Example 2 CYP