Question

a tower is 200√3 metre height find the angle of elevation of its top from a point on the ground 200 metre away from its foot​

Answer 1

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Answer 2

Given,

The height of a tower = 200√3 m

A point on the ground is 200 meters away from the foot of the tower.

To find,

The angle of elevation of the top of the tower from the point on the ground.

Solution,

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

Let us assume that the angle of elevation of the top of the tower from the point on the ground is x°.

According to the question;

The line joining the tip of the tower and the point on the ground forms the hypotenuse of a right-angled triangle whole perpendicular is represented by the height of the tower and the base is represented by the horizontal distance between the base of the tower and the point on the ground. The acute angle opposite to the perpendicular is x°.

So, on applying the Tan ratio for the angle x, we get;

Tan x° = (perpendicular)/(base)

=> (height of the tower)/(horizontal distance between the base of the tower and the point on the ground) = Tan x°

=> (200√3 m)/(200 m) = Tan x°

=> Tan x° = (√3)/1 = √3 = Tan 60°

=> x = 60°

=> angle of elevation of the top of the tower from the point on the ground = 60°

Hence, the angle of elevation of the top of the tower from the point on the ground is equal to 60°.