A spherical gas balloon of radius 16 meter subtends an angle 60 ° at the eye of the observer A while the angle of elevation of its center from the eye of A is 75 ° . Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :

Step-by-step solution

Assume, O is the centre of sphere and P , Q are the point of contact of tangents from A Let T be top most point of balloon & R be foot of perpendicular from O to ground. From triangle O A P ,   sin 30 ° = 16 O A ⇒ O A = 16 cosec 30 ° = 32 From triangle A R O ,   sin 75 ° = O R O A ⇒ O R = O A sin 75 ° ⇒ 32 ( 3 + 1 ) 2 2 = 8 6 + 8 2 So the height (in meter) of the top most point of the balloon from the level of the observer's eye is O R + O T = 8 ( 6 + 2 + 2 )