A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is 100 meters, sees the balloon at an angle of elevation of 30 o . If the balloon rises further vertically to a point where the angle of elevation as seen by the observer is 45 o , then its height (in meters) from the ground is (Take 3 = 1. 73 )

Question

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is 100 meters, sees the balloon at an angle of elevation of 30 o . If the balloon rises further vertically to a point where the angle of elevation as seen by the observer is 45 o , then its height (in meters) from the ground is (Take 3 = 1. 73 ),

MARKS App · Accepted Answer

Let A be the observer, P be the initial position of the balloon and it is at Q when the angle of elevation is 45 o From triangle A B P and triangle A B Q , ⇒ A B = 50 3 = B Q and B P = 50 So, P Q = B Q - B P = 50 3 - 1 = 50 0 . 73 = 36 . 5 meters

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