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in Trigonometry by (23.5k points)
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The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance 100 m from its base is 45°. If the angle of elevation of the top of the complete pillar at the same point is to be 60°, then the height of the incomplete pillar is increased by

(a) 50√2 m

(b) 100 m

(c) 100 (√3 - 1)m

(d) 100 (√3 + 1) m

1 Answer

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Best answer

(c) 100 (√3 - 1)m

Let BC be the incomplete pillar and BD be the complete pillar. 

In ΔABC, 

tan 45° = \(\frac{BC}{AB}\)

⇒ \(\frac{BC}{100}\) = 1 ⇒ BC = 100               ...(i)

In ΔABD, 

tan 60° = \(\frac{BD}{AB}\) ⇒ √3 = \(\frac{BC+x}{100}\) ⇒ \(x\) = 100√3 - BC

= 100√3 - 100 = 100 (√3 - 1)m.                     (∵ BC = 100 m)

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