Question 55
A pole is standing on the top of a house. Height of house is 25 metres. The angle of elevation of the top of house from point P is 45° and the angle of elevation of the top of pole from P is 60°. Point P is on the ground level. What is the height (in metres) of pole?
Solution
Let say, Pole's height is x and point P is m meter far from base of House.
$$\tan45^{\circ\ }=\frac{25}{m}.$$
or, $$m\ =25.$$
So, $$\tan60^{\circ\ }=\frac{25+x}{m}\ .$$
or, $$\sqrt{3}=\frac{25+x}{25}\ .$$
or, $$x=25\left(\sqrt{3}-1\right).$$
C is correct choice.
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