Three poles of heights

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

x

x+y

and

x+z

are posted at the vertices

A

B

and

C

of a triangular park of sides

a

b

and

c

, respectively. A plane sheet is mounted at the tops of the poles. If the plane of the sheet is inclined at an angle

\theta

to the horizontal plane, prove using vectors that

\theta = \tan^{-1} \left\{ \frac{\sqrt{\frac{y^2}{c^2} + \frac{z^2}{b^2} - \frac{2yz}{bc} \cos A}}{\sin A} \right\}.