Question

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30°$, which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle of depression of the car becomes $60°$. Find the height of the tower. (Use $\sqrt{3}=1.73$)

Solution

1

Tower DC of height h, car moves from A to B (50m), angles 30° and 60° from top D

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2

Let height of tower be $h$ m and $BC=x$ m. $\tan 60°=\frac{h}{x}\Rightarrow h=\sqrt{3}x$ ... (i)

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3

$\tan 30°=\frac{h}{x+50}\Rightarrow x+50=\sqrt{3}h$ ... (ii)

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4

From equation (i) & (ii): $x=25$ m, $h=25\sqrt{3}=43.25$ m

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