The angle of elevation and depression of the top and bottom of another building, measured from the top of a 24 m tall building, is 30° and 60°, respectively. Determine the second building's height.
The height of the second building H = h + 24
tan θ = \(\frac {opp}{adj}\)
tan 30\(^o = \frac {h}{x}\)
\(\implies\frac{\sqrt 3}{3} = \frac {h}{x}\)
\(\implies x = \sqrt 3 = 3h\)
\(\implies x = \frac {3h}{\sqrt 3}\) ....(i)
tan 60\(^o = \frac {24}{x}\)
\(\implies\sqrt 3 = \frac {24}{x}\)
\(\implies x\sqrt 3 = 24\)
\(\implies x = \frac {24}{\sqrt 3}\) ....(ii)
Equate equation (i) and (ii)
\(\implies \frac {3h}{\sqrt 3} = \frac {24}{\sqrt 3}\)
\(\implies\) 3h = 24
\(\implies h = \frac {24}{3}\) = 8m
∴The height of the second building = 8 + 24 = 32m
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