1. A person standing on top of a building looks down at an angle of depression of 30 degrees to see a car on the street below. If the building is 50 feet tall, how far away is the car from the building?
Let x be the distance from the building to the car.
tan(30 degrees) = 50 / x
x = 50 / tan(30 degrees)
x ≈ 86.60 feet
Therefore, the car is approximately 86.60 feet away from the building.
2. A plane flies at an elevation of 10,000 feet and spots a mountain at an angle of depression of 20 degrees. How far away is the mountain from the plane?
Let x be the distance from the plane to the mountain.
tan(20 degrees) = 10,000 / x
x = 10,000 / tan(20 degrees)
x ≈ 28,693.36 feet
Therefore, the mountain is approximately 28,693.36 feet away from the plane.
3. A person standing on a hill looks up at an angle of elevation of 15 degrees to see the top of a lighthouse. If the person is 100 feet away from the lighthouse and the hill is 20 feet tall, how tall is the lighthouse?
Let h be the height of the lighthouse.
tan(15 degrees) = (h + 20) / 100
h + 20 = 100 * tan(15 degrees)
h = 100 * tan(15 degrees) - 20
h ≈ 18.66 feet
Therefore, the lighthouse is approximately 18.66 feet tall.
Angles of Elevation and Depression Practice
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