Question

if a tower of height h is observed from a point with a distance d and angle theta , then express the relationship among h , d and theta​

Answer 1

Tan O = h / d is the correct answer.

Answer 2

Given:

The height of the tower = h

The distance between the tower and observer = d

The angle of elevation = θ

To Find:

The relation between 'd', 'h', and 'θ'.

Solution:

We can draw a triangle with one of the sides of being a tower, the other side is the distance of the observer from the foot of the tower, and the third side is a line joining the observer and the top of the tower.

Now, in the triangle

The tan of the angle of elevation (θ) = $\frac{perpendicular}{base}$

⇒ tan θ = $\frac{h}{d}$

Hence, we can say that the relation between h, d, and θ is tan θ = height of the tower ÷ distance of the observer from the foot of the tower.