Question

A girl is observing a ball from the balcony which is 30 m above from the ground (see the below figure) and the angle of depression of the ball is  such that sec3 = cosec2, find the distance of line of sight of ball.

Answer 1

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

Step-by-step explanation:

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​. = 100 m

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