Question

Q. The angle of elevation of the top of a tower as observed from a point on the ground is alpha
and on moving 'a' metres towards the tower, the angle of elevation is beta . Prove that the
height of the tower is a x tan alpha x tan beta whole divided by
tan beta - tan alpha

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Answer 1

The answer is as explained step by step in the above pic.

Answer 2

${\huge{\boxed{\bold{\red{\boxed{\frac{a.tanα.tanβ}\: {tanβ-tanα}}}}}}}$

$\huge\underline\mathfrak\purple{Answer}$

$\tan( \alpha ) = \frac{h. \tan( \beta ) }{a \tan( \beta ) + h } \\ \\ a \tan( \alpha ) . \tan( \beta ) + h \tan( \alpha ) = h \tan( \beta ) . \\ \\ h = \frac{a \tan( \alpha ). \tan( \beta ) }{ \tan( \beta ) - \tan( \alpha ) }$

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