On the top of a hemispherical dome of radius r there stands a flag of height h From a point on the g...........

Quantitative Aptitude (CDS) Coordinate Geometry

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^o. After moving a distance d towards the dome, when the flag is just visible, the elevation is 45^o. The ratio of h to r is equal to

$\small \sqrt{2}-1$