The elevation of a tower at a station A due North of it is `alpha` and at a station B due West of A is `beta` . Prove that height of the tower is `(A B sinalpha sinbeta)/(sin^2alpha-sin^2beta)` .

Explanation

`h=P A tan alpha`


therefore `{PA}={h} cot alpha`


and `h=P B tan beta`


therefore` {PB}={h} cot beta`


Also from the -angled triangle `P {AB}`, we get


`P B^{2}=P A^{2}+A B^{2}`


therefore `A B^{2}=P B^{2}-P A^{2}`


`=h^{2}(cot ^{2} beta-cot ^{2} alpha)`


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