Question

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

Answer 1

Given,

The height of tree = 39m

Angle of elevation of the top of the tree from point P = 60°

To find,

The distance between the base of the tree and the point P.

Solution,

We can easily solve this mathematical problem by using the following mathematical process.

Let, the top point of the tree = A

And, the bottom point of the tree = B

Now, AB = 39m

We have to calculate PB.

Here,we have to visualise the whole scenario as a right angle triangle.

Now we know that,

Height/Base = tan∅

39/PB = tan 60°

39/PB = √3

PB × √3 = 39

PB = 39/√3

PB = 13×3/√3

PB = 13√3

Hence, point P is 13√3 m away from the base of the tree.