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A contract was awarded to construct a vertical pillar at a horizontal distance of $100 m$ from a fixed point. It was decided that angle of elevation of the top of the complete pillar from this point to be $60 °$ . Contractor finished the job by making a pillar such that angle of elevation of its top was $45 °$ , Find the height of the pillar to be increased as per the terms of contract.

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73 m

75 m

77 m

70 m

answer is B.

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Detailed Solution

Given that a contract was awarded to construct a vertical pillar at a horizontal distance of

100 m

from a fixed point.
We have to find the height of the pillar.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for can be expressed as

tan θ = opposite adjacent

Suppose the height of the pillar be AC.
Then, by using the figure geometry,
Let BC be the incomplete pillar and BD be the complete pillar.
In

Δ ABC

tan 45 ° = B C A B ⇒ BC 100 =1 ⇒ BC = 100m

Δ ABD

tan 60 ° = B D A B ⇒ 3 = B C + x 100 ⇒ x = 1003 − BC ⇒ x = 1003 -100 (∵ BC = 100 m) ⇒ x = 100 (3 -1)m .

The height to be increased is

73 m

.
Therefore, the correct option is 2.

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