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A tree is leaning towards east. Two points due west of the tree are at distances ‘a’ and ‘b’ from its foot. If αand βare the elevations of the top of the tree from these points, its inclination to the horizon is

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a

Sin−1b−ab cotα−acotβ

b

Cos−1b−ab cotα−acotβ

c

Tan−1b−ab cotα−acotβ

d

Cot−1b−ab cotα−acotβ

answer is C.

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Detailed Solution

We have tanα=ha+x⇒a+x=hcotα -----xbAlso tanβ=hb+x⇒b+x=hcotβ -------xa⇒xb−a=hbcotα−acotβ⇒ hx=b−abcotα−acotβ∴tanθ=b−abcotα−acotβ ⇒θ=Tan−1b−abcotα−acotβ

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