Discussion
The angle of elevation of the top of a tower from a certain point is 300. If the observer moves 20 m towards the tower, the angle of elevation of the top of tower increases by 150. What is the height of tower?
Answer: C
The height of the tower is 27.3 m.
The angle rises from 30° to 45°. Let the height be \(h\) and the nearer distance \(x\). At 45°, \(h = x\). From the first point, 20 m further away:
\[ \begin{aligned} \tan 30^\circ &= \frac{h}{x + 20} = \frac{h}{h + 20} \\ \sqrt{3}\,h &= h + 20 \\ h &= \frac{20}{\sqrt{3} - 1} = \frac{20}{0.732} = 27.3 \end{aligned} \]
The trap is reading the second angle as 15°: the question says the angle increases by 15°, so it becomes 45°. 17.3 m is \(30 \tan 30^\circ\), a mix-up of the figures given.
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