Question

One skyscraper is 100 dm. At some time the shadow of a 1 dm high pole is 3√3 dm long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.

Answer 1

Let BC is a skyscraper of height 100 dm. and DE is a pole of height 9 dm.

Let elevation angle of sun is θ.

According to question, 

∠DAE = ∠CAB = θ and AE = 3√3 dm

From right angled ΔDEA

tan θ = DE/AE

= 9/3√3

= √3

= tan 60° 

⇒ θ = 60°

Hence, angle of elevation of sun = 60°

Again from right angled ΔABC,

tan θ = BC/AB

⇒ tan 60° = 100/AB

⇒ √3 = 100/AB

⇒ AB = 100/√3

Hence, angle of elevation of sun is 60° and length of shadow of skyscraper 100/√3 decimeter