Question

If a tower 30 m high, casts a shadow 10 root 3 m long on the ground, then what is the angle of elavation of the sun ?

Answer 1

Hey there!

Given,

Height of the tower (AB) = 30 m

Shadow of tower (BC) = 10√3 m

Let the angle of elevation of sun be Ф.

Now,

In ΔABC,

tan Ф =  Perpendicular / Base

tan Ф = AB / BC

tan Ф = 30 / 10√3

tan Ф = 3 / √3

On rationalizing,

tan Ф = √3

We know,

tan √3 = tan 60°

So,

tan Ф = tan 60°

Removing tan from both sides,

Ф = 60°

Hence, angle of elevation is 60°.

Hope It Helps You!

Answer 2

Given

Height of the tower H =30 m

Height of the shadow H₀ = 10√3 m

To determine the angle of elevation of the sun Θ = ?

Refer to the given figure.

From Δ ACB

tan Θ = AB/BC

Θ = tan⁻¹ (30/10√3 )

Θ = tan⁻¹ (√3)

Θ = 60⁰