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Q.

As seen from the top of fort of height a'' meters the angle of depression of the upper and the lower end of a lamp post are α and  βrespectively. The height of the lamp post is

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a

asinβ+αsinα.sinβ

b

acosβ+αcosα.sinβ

c

asinβ−αcosα.sinβ

d

acosβ−αsinα.sinβ

answer is C.

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Detailed Solution

tanβ=ax⇒x=acotβ, tanα=a−hx⇒x=a−hcotαacotβ=a−hcotα⇒h=acotα−cotβcotα=a.sinβ−acosα.sinβ
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