Section 8-7

Applications of Right Triangle Trigonometry

Suppose an operator at the top of a lighthouse sights a sailboat on a line that makes a 2° angle with a horizontal line. The angle between the horizontal and the line of sight is called an angle of _______________. At the same time, a person in the boat must look 2° above the horizontal to see the tip of the lighthouse. This is an angle of _______________.

depression

elevation

Examples:1. When the sun’s angle of elevation is 38°, a building casts a shadow of 45 m. How high is the building?

45 m38°

x

tan 38 °❑ =

𝑥451

x 35 mx (45)(tan 38°)

3. From the top of a lighthouse 20 m high, a sailboat is sighted having an angle of depression of 4°. How far from the lighthouse is the boat?

tan 4 °❑ =

20𝑦1

y 286 m

y(tan 4°) = 20

4°

4°tan 4° tan 4°y

20

2. Draw a diagram showing a person who is 1.5 m tall standing 20 m from the base of a building. Also show that the person sights the top of the building with an angle of elevation of 58°. Find the height of the building.

1.5 m

20 m

20 m1.5 m

z58°

tan 58 °❑ =

𝑧201

z 32 mz (20)(tan 58°)

32 m + 1.5 m33.5 m

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