Question

if the distance of a point from the tower is equal the height of the tower , then find the angle of elevation from the top of the tower from the points​

Answer 1

Correct Question :-

If the distance of a point from the tower is equal to the height of the tower, then find the angle of elevation of the top of the tower from that point.

Solution :-

A general approach would be an imaginary triangle which has its two sides equal i.e., Base and Perpendicular.

Here, we assumed the distance from the tower to that point to be the Base of the triangle and similarly, the height of the tower to be the Perpendicular of the triangle.

But It is a right triangle and the two sides of the triangle is equal i.e., Isosceles triangle.

Therefore, the angle opposite to these sides would also be equal because we know,

• Angles opposite to equal sides are equal.

So, Let that angle be θ, In the triangle, we have

⇒ Sum of all interior angles = 180°

⇒ θ + θ + 90° = 180° [because it is a right ∆]

⇒ 2θ = 90°

⇒ θ = 45°

Now, we can solve the same problem in much simpler way, we know

⇒ tan θ = Perpendicular / Base

But, Perpendicular = Base , So

⇒ tan θ = 1

⇒ θ = 45° [∵ tan 45° = 1]

Hence, The angle of elevation would be 45°.