Angle of Depression

Geometry Level 2

A surveyor determines that the angle of elevation from a transit to the top of a building is x° = 27.7°. The transit is positioned 5.5 feet above ground level and 135 feet from the building, that is c = 5.5 feet and b = 135 feet. Find the height of the building to the nearest tenth of a foot.


The answer is 76.98.

Niña Sibal by Niña Sibal , 24, Philippines

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4 solutions

Hey yo,

As the height of the building = (135 Tan (27.7) ) + 5.5 = 76.38 feets...

Thanks ah....

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Francis Solis Jr.
Mar 20, 2014

I remember the formula that until now i still cant forget. The SOH, CAH, TOA. In this problem, we are given the angle and its Adjacent side and we will look for the opposite side which must be added to 5.5. So we must use the TOA formula.

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Fhil Caballar
Mar 6, 2014

use tangent......tan27.7=x-.5.5/135.............x-55 because only a portion of building is intercepted by the angle

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Manohar Mathur
Mar 4, 2014

Let height of building from transit height = H feet. Then, tanxo=H/135 = tan27.5o= 0.52 So, H = 135*0.52=70.2 Building height from ground = H+5.5=70.2+5.5=75.7 feet

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