A pole stands vertically on a road, which goes in the north-south direction. P, Q are two points towards the north of the pole, such that PQ = b, and the angles ofelevation ofthe top ofthe pole at P, Q are a, B respectively. Then the height of the pole is:

A

$$\frac{b}{\tan \beta + \tan \alpha}$$

B

$$\frac{b}{\cot \beta - \cot \alpha}$$

C

$$\frac{b}{\tan \beta - \tan \alpha}$$

D

$$\frac{b \tan \alpha}{\tan \beta}$$