The angle of elevation of top of tower from a point A due south of the tower is - and from a point B due East of the tower is - If A B-d- then the height of tower isA- d- 2- 2-B- d-tan 2-tan 2-C- d- 2- 2-D- d-tan 2-tan 2-

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Standard XII

Mathematics

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The angle of ...

Question

The angle of elevation of top of tower from a point A due south of the tower is $α$ and from a point B due East of the tower is $β$ . If AB = d, then the height of tower is

\frac{d}{\sqrt{t a n^{2} α - t a n^{2} β}}

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\frac{d}{\sqrt{t a n^{2} α + t a n^{2} β}}

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\frac{d}{\sqrt{c o t^{2} α + c o t^{2} β}}

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\frac{d}{\sqrt{c o t^{2} α - c o t^{2} β}}

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Solution

The correct option is C $\frac{d}{\sqrt{c o t^{2} α + c o t^{2} β}}$

$∵ O B = h c o t β a n d O A = h c o t α$
Then $O B^{2} + O A^{2} = h^{2} c o t^{2} β + h^{2} c o t^{2} α d^{2} = h^{2} (c o t^{2} α + c o t^{2} β) \Rightarrow h^{2} = \frac{d^{2}}{c o t^{2} α + c o t^{2} β} \Rightarrow h = \frac{d}{\sqrt{c o t^{2} α + c o t^{2} β}}$

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The angle of elevation of top of tower from a point A due south of the tower is α and from a point B due East of the tower isβ. If AB = d, then the height of tower is

The correct option is C d√cot2α+cot2β ∵OB=h cot βandOA=h cotα Then OB2+OA2=h2 cot2β+h2 cot2αd2=h2(cot2α+cot2β)⇒h2=d2cot2α+cot2β⇒h=d√cot2α+cot2β

The angle of elevation of top of tower from a point A due south of the tower is $α$ and from a point B due East of the tower is $β$ . If AB = d, then the height of tower is