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
HOMEWORK:page 318 #2-10 even
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