Draw and solve the pictures presented by the information given.
1. The angle of elevation of the top of the building from a point 30 meters away from the building is 65°.
2. The angle of depression of a boy from a point on a lighthouse 30.5 meters above the surface of the water is 3°.
3. If an airplane that is cruising at an altitude of 9 km wants to land at NAIA, it must begin its descent so that the angle of depression to the airport is 7º
4. A bird sits on top of a 5-meter lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35º.
1. The angle of elevation of the top of the building from a point 30 meters away from the building is 65°.
2. The angle of depression of a boy from a point on a lighthouse 30.5 meters above the surface of the water is 3°.
3. If an airplane that is cruising at an altitude of 9 km wants to land at NAIA, it must begin its descent so that the angle of depression to the airport is 7º
4. A bird sits on top of a 5-meter lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35º.
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Verified answer
Answer:
1 To find the height of the building, we can use the tangent function. Let's denote the height of the building as h.
tan(65°) = h / 30
Using a scientific calculator or tangent table, we can find:
h = 30 * tan(65°)
h ≈ 80.82 meters
Therefore, the height of the building is approximately 80.82 meters.
2 To find the distance between the boy and the lighthouse, we can use the tangent function. Let's denote the distance as d.
tan(3°) = (30.5) / d
Using a scientific calculator or tangent table, we can find:
d = (30.5) / tan(3°)
d ≈ 1011.99 meters
Therefore, the distance between the boy and the lighthouse is approximately 1011.99 meters.
3 To find the horizontal distance between the airplane and NAIA, we can use the tangent function. Let's denote the horizontal distance as d.
tan(7°) = 9 / d
Using a scientific calculator or tangent table, we can find:
d = 9 / tan(7°)
d ≈ 76.38 km
4 Therefore, the horizontal distance between the airplane and NAIA is approximately 76.38 km.
To find the distance between the observer and the lamppost, we can use the tangent function. Let's denote the distance as d.
tan(35°) = 5 / d
Using a scientific calculator or tangent table, we can find:
d = 5 / tan(35°)
d ≈ 6.67 meters
Therefore, the distance between the observer and the lamppost is approximately 6.67 meters.
Step-by-step explanation: