A spherical gas balloon of radius 16 meter subtends an angle 60[^] at the eye of the obser…

Question

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

Accepted Answer

O $$\to$$ centre of sphere

P, Q $$\to$$ 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 OAP, OA = 16cosec30$$^\circ$$ = 32

From triangle ABO, OR = OA sin75$$^\circ$$ = $$32{{\left( {\sqrt 3  + 1} \right)} \over {2\sqrt 2 }}$$

So level of top most point = OR + OT

$$ = 8\left( {\sqrt 6  + \sqrt 2  + 2} \right)$$

Solutions · 1