Two men on either side of a temple of 30 m height observe its top at the angles of elevation 30∘ and 60∘ respectively. Find the distance between the two men.

# Two men on either side of a temple of 30 m height observe its top at the angles of elevation 30∘ and 60∘ respectively. Find the distance between the two men.

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### Solution:

Let AB be the height of the temple and P and Q are the two men on either side of the temple.

Given that,

In △ABP,

$\mathrm{tan}\left(\angle APB\right)=\frac{AB}{PB}$

$\mathrm{tan}30°=\frac{30}{PB}$

In △ABP,

$\mathrm{tan}\left(\angle AQB\right)=\frac{AB}{QB}$

$\mathrm{tan}60°=\frac{30}{QB}$

$QB=\frac{30}{\sqrt{3}}$

Now, PQ = PB + QB =

So, PQ =

Therefore, distance between two men, i.e. PQ =

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