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# Right Triangle Trigonometry Help (page 2)

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By McGraw-Hill Professional
Updated on Sep 6, 2011

#### Examples

• A person is standing 300 feet from the base of a five-story building. He estimates that the angle of elevation to the top of the building is 63°. Approximately how tall is the building?

We need to find b in the following triangle.

Fig. 13.39

We could use either of the ratios that use the opposite and adjacent sides, tangent (opposite/adjacent) and cotangent (adjacent/opposite). We will use tangent.

This gives us the equation tan 63° = b /300. When we solve for b , we have b = 300 tan 63° ≈ (300)1.9626 ≈ 588.78. The building is about 589 feet tall.

• A guy wire is 60 feet from the base of a tower. The angle of elevation from the top of the tower along the wire is 73°. How long is the wire?
• We need to find c in the following triangle.

Fig. 13.40

We could use either cosine (adjacent/hypotenuse) or secant (hypotenuse/adjacent). Using cosine, we have cos 73° = 60/ c . Solving this equation for c gives us c = 60/cos 73° ≈ 60/0.2924 ≈ 205. The wire is about 205 feet long.

## Right Triangle Trigonometry Practice Problems

#### Practice

1. Find all six trigonometric ratios for θ.

Fig. 13.41

2. Solve the triangle.

Fig. 13.42

3. A plane is flying at an altitude of 5000 feet. The angle of elevation to the plane from a car traveling on a highway is about 38.7°. How far apart are the plane and car?

#### Solutions

1.

2. We could use any of the ratios involving the hypotenuse. We will use cosine: cos 60° = a /4. Since cos 60° = 1/2, we have 1/2 = a /4. Solving for a gives us a = 2.

3. We need to find c in the following triangle.

Fig. 13.43

Practice problems for this concept can be found at: Trigonometry Practice Test.

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