Question 95

- The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar must be raised so that its angle of elevation at the same point may be 45°, is (takeing √3 = 1.732)

Solution

In $$\triangle ABC , \tan 30 \degree = \frac{AB}{BC}

$$\frac{1}{\sqrt{3}} = \frac{AB}{150}

AB = 86.6 m

In $$\triangle DBC , \tan 45 \degree = \frac{DB}{BC}

$$1 = \frac{AD + AB}{BC}

BC = AD + 86.6

AD = 150 -86.6 = 63.4

So, the answer would be option a)63.4

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