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A building subtends a right angle at the top of a pole on the other side of the road. The line joining the top of the pole and the top of the building makes an angle of $60 °$ with the vertical. If the width of the road is 45 m, then what will be the height of the building?

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303

603

602

302

answer is B.

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Detailed Solution

Given that,
A building suspends a right angle at the pole on the other side of the road
We draw a diagram,
Question Image

We use

tan θ = h e i g h t b a s e

in the triangle BED,

⇒ tan 30 ° = B E D E ⇒ B E = D E × tan 30 °

Substituting the value

D E = 45

and using

tan 30 ° = 13

⇒ B E = 453

……(1)
We use the tangent of an angle in the triangle AED,

⇒ tan 60 ∘ = A E D E ⇒ A E = D E × tan 60 ∘

Substituting the value

D E = 45

and

tan 60 ° = 3

⇒ A E = 453

……(2)
Now we add the equation (1) and (2),

⇒ B E + A E = 453 + 453 ⇒ A B = 45 + 45 × 3 3 ⇒ A B = 1803 ⇒ A B = 603 m

Thus the height of the building will be

603

m.
Therefore the correct option is 2.

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