A statue 4 metres high sits on a column 5.6 metres high. How far from the column must a man,whose eye level is 1.6 metres from the ground, stand in order to have the most favourable view of the statue.

Explanation

`tanalpha=4/x`

`tan(theta+alpha)=8/x`

`(tantheta+tanalpha)/(1-tantheta*tanalpha)=8/x`

`(tantheta+4/x)/(1-4/x*tantheta)=8/x`

`tantheta+4/x=8/x=32/x^2tantheta`

`tantheta+32/x^2tantheta=8/x-4/x`

`tantheta(1+32/x^2)=4/x`

`tantheta=(4/x)/(1+32/x^2)`

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