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Question 80
P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are $$60^\circ$$ and $$30^\circ$$, respectively and the distance between them is $$84\sqrt3$$ m. What is the height (in m) of the pole?
Solution
In $$\triangle POC$$,
$$\tan 60$$ = $$\frac{\sqrt{3}}{1} = \frac{OC}{OP}$$
$$\frac{OC}{OP} = \frac{3}{\sqrt{3}}$$
In $$\triangle QOC$$,
$$\tan 30$$ = $$\frac{1}{\sqrt{3}} = \frac{OC}{OQ}$$
$$\frac{OC}{OQ} = \frac{3}{3\sqrt{3}}$$
OC = 3 units
PQ = OP + OQ =Â $$\sqrt{3} + 3\sqrt{3} = 4\sqrt{3}$$ units
$$84\sqrt3 =Â 4\sqrt{3}$$Â units
1 unit = 21 m
3 unit = 63 m
Height of the pole = 63 m
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