Question

The length of the shadow of a vertical pole is `sqrt(3)` times its height. Find the angle of elevation of sun.

Answer 1

Given: A vertical pole of height h casts a shadow of length `sqrt(3) xx h` and θ is the angle of elevation of the sun.

Step-wise calculation:

1. Let pole = h and shadow = `sqrt(3) xx h`.

2. In the right triangle.

`tan θ = "Opposite"/"Adjacent"` 

= `h/(sqrt(3) xx h)`

3. `tan θ = 1/sqrt(3)`

= tan 30°

4. Therefore, θ = 30°.

The angle of elevation of the sun is 30°.