The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be $\;\alpha\;$ . After moving a distance 2 meters from P towards the foot of the tower , the angle of elevation changes to $\;\beta\;$. Then the height (in meters) of the tower is :

Question

$(a)\;\large\frac{2 sin \alpha sin \beta}{sin(\beta-\alpha)}\qquad(b)\;\large\frac{ sin \alpha sin \beta}{cos(\beta-\alpha)}\qquad(c)\;\large\frac{2 sin(\beta-\alpha)}{sin \alpha sin\beta }\qquad(d)\;\large\frac{cos(\beta-\alpha)}{sin \alpha sin \beta }$