Question 1044493: A window on the fourth floor of a building is 20 m above the ground. From the window, the angle of depression to the base of a nearby building is 31 degrees and the angle of elevation to the top of the buildings is 40 degrees. How tall is the nearby building to the nearest metre?
Answer by Boreal(15235)   (Show Source):
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|----------------------------40
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|---------------------------31 deg
|---------------------------59 deg
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From the angle of depression, it is 20 m to the ground, adjacent. We are assuming the lower part of the building is 20 m tall. Using that, the distance directly to the building is tan 31=20/x, where x is adjacent side and the distance to the building. The angle of depression is the part of the triangle we need here. x=20/tan 31=33.29 m.
Using that distance, the tangent of 40 degrees is opposite over adjacent, and adjacent is 33.29 m
tan 40=x/33.29
33.29*tan 40=x
x=27.93 m.
The height of the building is 47.93 m,
48 m.
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