From a point P on a level ground the angle of elevation of the top of the tree is 60° if the tree is 39 m high how far is its base from P ?

Let x be the distance from point P to the base of the tree.

Since the angle of elevation from point P to the top of the tree is 60°, we can create a right triangle with the height of the tree (39 m) as the opposite side and the distance x as the adjacent side.

Using trigonometry, we can use the tangent function to find the distance x:

tan(60°) = opposite/adjacent
tan(60°) = 39/x

Solving for x:

x = 39 / tan(60°)
x = 39 / √3
x = 13√3

Therefore, the base of the tree is approximately 22.5 meters away from point P.

Let the distance of the tree from the point P be x metres.

From the given data, we have

tan 60° = (39 / x)
⇒ √3 = (39/x)

⇒ x = 39 / √3
⇒ x = 39 - √3 / 3
⇒ x = 22.63 m

Therefore, the base of the tree is 22.63 metres away from the point P.