Determine the height of a mountain if the elevation of its top at an unknown distance from base is `25^@ 10'` and at a distance of 5 km further off from the mountains, along the same line the angle of elevation is `15^@20'` Give the answer in km correct to 2 decimals.

Explanation

`tantheta=h/x`

`x=h/tantheta`

`tanphi=h/(5+x)`

`5+x=h/tanphi`

`5+h/tantheta=h/tanphi`

`5=h/tanphi-h/tantheta=hcotphi-hcottheta`

`5=h(cosphi-cottheta)`

`5=h*1.52`

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