An observer, 1.5 m tall, is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Determine the height of the chimney?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30 m
The angle of elevation is measured from the observer’s eye, which is 1.5 m above the ground. So \(\tan45^\circ\) gives only the part of the chimney above eye level, and the observer’s height is added to it.
In the right triangle EBA, \(\displaystyle \tan45^\circ=\frac{AB}{EB}=\frac{h}{28.5}\)
\(\tan45^\circ=1\), so \(h=28.5\,\mathrm{m}\)
Height of the chimney \(=28.5+1.5=30\,\mathrm{m}\)