The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation

Question

The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top from the same point will be:

Accepted Answer

Let the original height be $h$ and distance be $x$. $	an 30^\circ = \frac{h}{x} = \frac{1}{\sqrt{3}} \implies x = h\sqrt{3}$. When height is doubled ($2h$), let the new angle be $	heta$. Then $	an 	heta = \frac{2h}{x} = \frac{2h}{h\sqrt{3}} = \frac{2}{\sqrt{3}}$. Thus, $	heta = 	an^{-1}\left(\frac{2}{\sqrt{3}}ight)$, which is less than 60° and more than 45°, so it is not doubled.

Applications of Trigonometry

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