The angle of elevation and depression of the top and bottom of another building, measured...
MATHEMATICS
JAMB 2023
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.
- A. 24 m
- B. 32\(\sqrt3\) m
- C. 24\(\sqrt3\)
- D. 32 m
Correct Answer: D. 32 m
Explanation
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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