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The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80mts towards the top, the slope inclined at an angle of 30° to the horizontal plane, the angle of elevation of the top of the hill becomes 75°. Then, the height of the hill (in mts) is _________

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answer is 80.

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Detailed Solution

$\begin{array}{l} ∵ \underline{BCA} = 45^{\circ} h = AC . \\ \sin 30^{\circ} = \frac{y}{80} \Rightarrow y = 40 \\ \cos 30^{\circ} = \frac{x}{80} \Rightarrow x = 40 \sqrt{3} \\ \tan 45^{\circ} = \frac{h - y}{h - x} \Rightarrow h = 80 \end{array}$

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