If two towers of height $h_{1}$ and $h_{2}$ subtend angles $45^{\circ}$ and $30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of $h_{1} : h_{2}$ .

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Solution

The correct option is C
Let $h_{1}$ and $h_{2}$ be the heights of the tower and $2 x$ be the total distance between the towers.

From the above figure,
$t a n 45^{\circ} = \frac{h_{1}}{x} . . . . (1) t a n 30^{\circ} = \frac{h_{2}}{x} . . . . (2) \Rightarrow \frac{t a n 45^{\circ}}{t a n 30^{\circ}} = \frac{\frac{h_{1}}{x}}{\frac{h_{2}}{x}} h_{1} : h_{2} = \sqrt{3} : 1$

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If two towers of height h1 and h2 subtend angles 45∘ and 30∘ respectively at the midpoint of the line joining their feet, then find the ratio of h1:h2.

The correct option is C Let h1 and h2 be the heights of the tower and 2x be the total distance between the towers. From the above figure, tan 45∘=h1x....(1)tan 30∘=h2x....(2)⇒tan 45∘tan 30∘=h1xh2xh1:h2=√3:1

If two towers of height $h_{1}$ and $h_{2}$ subtend angles $45^{\circ}$ and $30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of $h_{1} : h_{2}$ .