Question

if the angle of elevation of the top of a coconut tree from a point on the ground is 60° and the point is 20 metre away from the foot of the tree, let is find the height of the tree.

Answer 1

Step-by-step explanation:

Let's ,C be the point where the person is standing.

AB is the coconut tree

CB is 20 Mt

Angle of elevation at the top of the coconut tree to the point where the person is standing at 60° .

Now,

tan theta = perpendicular/base

tan 60°= AB/BC

√3=AB/20Mt

AB=20√3 Mt .

Answer 2

Given,

The angle of elevation of the top of a coconut tree from a point on the ground is 60°.

The point is 20 meters away from the foot of the tree.

To find,

The height of the tree.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the height of the coconut tree is x meters.

Now, according to the question;

The imaginary line joining the top of the coconut tree with the point on the ground forms the hypotenuse of an imaginary right-angled triangle whole perpendicular is represented by the height of the coconut tree and the base is represented by the horizontal distance between the base of the tree and the point on the ground. The acute angle opposite to the perpendicular is 60°.

Now,

As per trigonometry, on applying the Tan ratio formula for the given angle, we get;

Tan 60° = (perpendicular)/(base)

=> (height of the coconut tree)/(horizontal distance between the base of the tree and the point on the ground) = √3

=> (x m)/(20 m) = √3

=> x = 20√3 m

=> height of the coconut tree = 20√3 m

Hence, the height of the coconut tree is equal to 20√3 m.