On the top of a hemispherical dome of radius r, there stands a flag of height h.From a point on the ground the elevation of the top of the flag is `30^@`. After moving a distance 'd' towards dome,when the flag is just visible,then elevation is `45^@`. The value of r and h is:

Explanation

`tan30^0=(h+r)/(r+x+d)-(1)`

`tan45^0=(h+r)/(r+x)`

`1=(h+r)/(r+x)`

`x=h`

`sin45^0=r/(r+x)`

`1/sqrt2=r/(r+x)`

`r+x=sqrt2r`

`x=(sqrt2-1)r`

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