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Home Q & A Board Science-Related Homework Help Mathematics
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Heybonita Heybonita
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A year ago
A window in an apartment building is 32 m above the ground.

From the window, the angle of elevation to the top of a second apartment building across the street is 36°.

From the same window, the angle of depression to the bottom of the apartment building across the street is 47°

Determine the height of the apartment across the street.  Show your process.
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#1
A year ago Edited: A year ago, bio_man
Draw a horizontal from the window to the apartment building, label A
at the window and B at the apartment. Let k be the height from that line to the top of the apartment building.

in the bottom triangle:
tan 47° = 32/AB
AB = 32/tan47

In the top triangle:
 tan 36 = h/AB
h = ABtan36 = 32tan36/tan47 = 24.93

So height of apartment building = 32 + 24.93 = 56.93

The window is already 32 m above the ground, and we have
an angle of elevation  to the top of the building
So the answer of course must be greater than 32 m
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