Question

If a tower 30 m high, casts a shadow `10sqrt3` m long on the ground, then what is the angle of elevation of the sun?

Answer 1

Let AB be the tower and BC be the length of the shadow of the tower. Suppose the angle of elevation of the sun from the ground be θ.

It is given that AB = 30 m and BC = `10sqrt3` m

In ∆ABC

`tan theta = (AB)/(BC)`

`=>tan theta = 30/(10sqrt3)`

`=> tan theta = 3/sqrt3`

`=> tan theta = sqrt3`

`=> theta = 60^@`                    (∵ `tan 60^@ = sqrt3`)

Thus, the angle of elevation of the sun is 60°