Two buildings are 200ft apart. The height of the taller building is 135ft. The angle of depression from the top of the taller building to the top of the shorter building is 7 degrees. How do you find the height of the shorter building to the nearest foot?

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Answer 1 · 2017-03-30T19:23:21

$= 110.4$ $= 110.4$ ft

Let the difference in heights of the buildings be $x$ $x$ ft

The buildings are $200$ $200$ ft apart - all the way up from the ground to the top of the buildings.

Draw in a triangle joining the tops of the buildings and show the angle of depression as $7°$

Le'ts find $x$ :

$x/200 = tan 7$

$x = 200 xx tan 7$

$x = 24.557$ ft

This is the difference in the heights of the buildings.

Height of shorter building = $135-24.6$ ft

$= 110.4$ ft