Problem on sine rule Type:-2
(i)The angle of elevation of the top of the tower from a point A due South of the tower is α and from B due east of the tower is β. If AB=d Show that the height of the tower is `d/(cot^2α+cot^2β)`
(ii) A tree stands vertically on a hill side which makes an angle of `15^∘` with the horizontal. From a point on the ground 35m down the hill from the base of the tree ; the angle of elevation of the top of the tree is `60^∘` .find the height of the tree ?

Explanation

Let `mathrm`{OP} be the tower and let `mathrm{A}` and `mathrm{B}` be two points due south and east respectively of the tower such that
``
angle mathrm{OAP}=alpha
``
and `angle mathrm{OBP}=beta`.
Let `mathrm{OP}=mathrm{h}`
In `triangle mathrm{OAP}`, we have
`tan alpha=frac{mathrm{h}}{mathrm{OA}}`
...