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From the top of a 150 m tall building A, the angle of elevation to the top of the building B is 45 degrees and the angle of depression to the bottom of the building B is 30 degrees. What is the height of the building B?

From the top of a 150 m tall building A, the angle of elevation to the top of the building B is 45 degrees and the angle of depression to the bottom of the building B is 30 degrees. What is the height of the building B? Correct Answer 150 (1 + √3) m

Calculation:

From the given information the diagram can be drawn as

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Let XY be the length of building A

PQ be the length of building B

XP = YR

In ΔXYP

tan 30° = XY/XP

1/√3 = 150/XP

⇒ XP = 150√3 m

Now,

In Δ QYR

tan 45° = QR/YR

1 = QR/150√3

⇒ QR = 150√3

∴ Height of building B

⇒ PQ = QR + PR = 150 + 150√3

⇒ PQ = 150 (√3 + 1)

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