A palm tree stands on the bank of a river. A post is fixed in the earth on the other bank just opposite to the palm tree. On moving ` 7sqrt(3)` metres from the post along the bank, it is found that the tree makes an angle of `60^(@)` at that point with respect to this bank. Find the width of the river.

Explanation

Let the width of the river be AB. A is the position of palm tree and B is the position of the post.
As per question.
if BC = `7sqrt(3)` m, then `angleACB = 60^(@)`.
Now, from the right-angled triangle ABC, we get,
`tan 60^(@) = (AB)/(BC)`
or, `sqrt(3) = (AB)/(7sqrt(3)) " " or, " " AB = sqrt(3)xx7sqrt(3)` or, AB = 21.
Hence the width of the river is 21 metres.