Question 93

- If the angle of elevation of the sun decreases from $$45^\circ$$to $$30^\circ$$, then the length of the
shadow of a pillar increases by 60m. The height of the pillar is

Solution

Let AB be the height of the pole = h m

CD = 60 m

In $$\triangle ABC$$,

$$\tan 45\degree = \frac{AB}{AC} =>1 = \frac{h}{BC} => BC = h m

In $$\triangle ABD$$,

$$\tan 30\degree = \frac{AB}{BD}$$

$$\frac{1}{\sqrt{3}} = \frac{h}{h+60}$$

$$ h = \frac{60}{\sqrt{3} - 1} = 30(\sqrt{3} + 1)$$

So , the answer would be option c)30($$\surd{3}$$+1) m

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