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

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

Key Concept

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

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

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

Use Tangent to find Missing Lengths Substitution Multiply each side by 20. ENTER × TAN 20 40 16.78199262 Use a calculator. x  16.8 Simplify. Answer: The building is about 16.8 meters tall. Example 2

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. 34.7 meters D. 272.7 meters Example 2 CYP