question_answer

A and B are two points in the horizontal plane through O. the foot of pillar OP of height h such that\[\angle AOB=\theta \]. If the elevation of the top of the pillar form A and B are also equal to \[\theta \], then AB is equal to

A) \[h\cot \theta \]

B) \[h\cos \theta \sec \frac{\theta }{2}\]

C) \[h\cot \theta \sin \frac{\theta }{2}\]

D) \[h\cos \theta \cos ec\frac{\theta }{2}\]  

Correct Answer: B

Solution :

[b] \[OA=OB=h\cot \theta \] Now, \[AB=2AN=2AO\sin \frac{\theta }{2}\] \[=2h\frac{\cos \theta }{\sin \theta },\sin \frac{\theta }{2}=h\cos \theta \sec \frac{\theta }{2}\]