Question : Two persons are on either side of a temple, 75 m high, observe the angle of elevation from the top of the temple to be 30° and 60°, respectively. The distance between the persons is:
Option 1: 173.2 metres
Option 2: 100 metres
Option 3: 157.7 metres
Option 4: 273. 2 metres
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Correct Answer: 173.2 metres
Solution : Clearly from the figure the distance $BD$ is $(BC+CD)$. In $\triangle ABC$, $\tan 30°=\frac{AC}{BC}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{75}{BC}$ ⇒ $BC=75\sqrt{3}$ metres In $\triangle ACD$, $\tan 60°=\frac{AC}{CD}$ ⇒ $\sqrt{3}=\frac{75}{CD}$ ⇒ $CD=\frac{75}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}$ ⇒ $CD=25\sqrt{3}$ metres Distance between both persons $BD=BC+CD$ = $75\sqrt{3}+25\sqrt{3}$ = $100\sqrt{3}=100\times1.732=173.2$ metres Hence, the correct answer is $173.2$ metres.
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