From a window 30 meters above the ground, John finds that the angle of elevation of the top of a monument is 10 degrees and the angle of depression of the foot of the monument is 20 degrees. What is the height of the monument?

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Dereon Parker · Accepted Answer

Let the distance between the monument and the window be x.    Then we get,    tan  ⁡      20          ∘        =      30    x      x  =      30          tan      ⁡              20                  ∘                        x  =  82.42     Moreover we get,        y    82.42    =  tan  ⁡      10          ∘          y  =  82.42  ×  tan  ⁡      10          ∘          y  =  14.53     Thus the height of the monument is:    =  30  +  14.53    =  44.53     m     Hence the height of the monument is 44.53 meters.

From a window 30 meters above the ground, John finds that the angle of elevation of the top of a monument is 10 degrees and the angle of depression of the foot of the monument is 20 degrees. What is the height of the monument?

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