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A flag pole '\(h\)' metres is on the top of the hemispherical dome of radius '\(r\)' metres. A man is standing \(7 \ m\) away from the dome. Seeing the top of the pole at an angle of \(45^{\circ}\) and moving \(5 \ m\) away from the dome and seeing the bottom of the pole at an angle of \(30^{\circ}\). Find (i) the height of the pole (ii) radius of the dome. (\(\sqrt{3} = 1.732\))
 
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Answer:
 
(i) The height of the pole is  \(m\).
 
(ii) The radius of the dome is  \(m\).