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Question 94
From a point exactly midway between the foot of two towers P and Q,the angles of elevation of their tops are $$30^\circ$$ and $$60^\circ$$, respectively. The ratio of the height of P to that of Q is:
Solution
AO = OB
In $$\triangle AOP$$,
$$tan30\degree = \frac{AP}{AO}$$
$$\frac{1}{\sqrt{3}}Â = \frac{AP}{AO}$$
AP = 1
AO = $$\sqrt{3}$$
In $$\triangle AOP$$,
$$tan60\degree = \frac{BQ}{BO}$$
$$\frac{\sqrt{3}}{1} = \frac{BQ}{BO}$$
$$\frac{BQ}{BO} = \frac{3}{\sqrt{3}}$$
BQ = 3
BO = $$\sqrt{3}$$
The ratio of the height of P to that of Q = 1 :Â 3
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