A window washer on a ladder looks at a nearby building 126 ft​ away, noting that the angle of elevation to the top of the building is 18.4 degrees and the angle of depression to the bottom of the building is 8.4 degrees . How tall is the nearby​ building?

1 Answer
Richard G.
Mar 13, 2018

#60.52 ft#

Explanation:

The building is the opposite side of the triangle compared to the measured angles, and the distance of the ladder to the building (126 ft) is the adjacent side of the triangle. The trigonometric formula for opposite compared to adjacent is tan.

tan = opposite / adjacent, so to solve for the opposite side, rearrange the formula: opposite = tan x adjacent.

#o=tan(18.4)*126ft=0.3326557*126ft=41.915ft#

and #o=tan(8.4)*126ft=0.147667*126ft=18.606ft#

The total height of the building is the sum of these two numbers,
#ht=41.915ft+18.606ft=60.52ft#

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