Question

A girl is observing a ball from the balcony which is 30 metres above from the ground( see the above figure) and the angle of depression of the ball is A .Such that sec3A equals to cosec2A , find the distance of line of sight of ball​.

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Answer 1

Answer:

Sec3A = Cosec2A

=> 1/Cos3A = 1/Sin2A

=> Sin2A  = Cos3A

=> Sin2A = Sin(90 - 3A)

=> 2A = 90 - 3A

=> 5A = 90

=> A = 18

SinA = BC/AC

=> AC = BC/Sin18

=> AC = 30/Sin18

=> AC = 30/0.3

=> AC = 100

the distance of line of sight of ball. = 100m.

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