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.
The robot tutor's answer is just so much gibberish.
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 robot's answer is seen to be ridiculous immediately.
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
Let h be the height of the apartment building across the street.
We can use the tangent function to solve for h.
tan(36°) = h/32
h = 32tan(36°)
h = 28.7 m