The angle of elevation of the top of a hill from each of the verticles A,B,C of a horizontal triangle is `alpha`. The height of the hill is `1. b tan α cosec β 2. 1 2 a tan α cosec A 3. 1 2 c tan α cos e c C` 4. none of these

Options

A. b tan `alpha` cosec `beta`
B. `1/2` a tan `alpha` cosec A
C. `1/2c tan alpha cosec C`
D. none of these

Answer

B

Explanation

Clearly , the foot of the tower is the circumcentre of `triangleABC`.Let R be the circum-radius of `triangleABC`. Then,
`R=h cot alpha`
`rArr a/(2 sin A)=h cot alpha rArr h=a/2 tan alpha cosec A`