question_answer

A vertical pole stands at a point A on the boundary of a circular park of radius a and subtends an angle \[\alpha \] at another point B on the boundary. If the chord AB subtends an angle \[\alpha \] at the centre of the park, then the height of the pole is

A) \[2a\sin \frac{\alpha }{2}\tan \alpha \]  

B)        \[2a\cos \frac{\alpha }{2}\tan \alpha \]

C) \[2asin\frac{\alpha }{2}\cot \alpha \]     

D)        \[2a\cos \frac{\alpha }{2}\cot \alpha \]

Correct Answer: A

Solution :

   [a] \[AB=2a\,\,\sin \frac{\alpha }{2}\] In \[\Delta ABC,\] \[\tan \alpha =\frac{AC}{AB}\] \[\therefore \,\,\,\,AC=2a\,\,\sin \frac{\alpha }{2}\tan \alpha \]