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Question

From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be α &  β. The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is



A

Tan α+Tan βTan α. Tanβ

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B

Tan αTan βTan α .Tan β

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C

Tan α.TanβTan α+Tan β

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D

Tan α.Tan βTan αTanβ

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Solution

The correct option is B

Tan α.TanβTan α+Tan β


Let H be the height at which the aeroplane is flying.

In triangle ABD

tanβ=ADBD=HBDBD=Htan β                 (i)

In ADC

tan α=ADDC=HDCDC=Htan α            (ii)

Now, BD + DC = BC = 1 m

Htan β+Htan α = 1

H[1tan β+1tan α]=1H[tan α+tan βtan α.tanβ]=1H=tan α.tanβtan α+tan β


Mathematics

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