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 the dome, when the flag is just visible, the elevation is 45°. The ratio of h to r is equal to

• A. √2 – 1
• B. \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}\)
• C. \(\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}d\)
• D. \(\frac{{\left( {\sqrt 3 + 1} \right)\left( {\sqrt 2 - 1} \right)}}{{2\sqrt 2 }}d\)