Question

If the ratio of the height of a tower and the length of its shadow is √3 :1, what is the angle of elevation of the Sun?

Answer 1

Answer:

The angle of elevation of the tower is 60°.

Step-by-step explanation:

• In the attached figure below, AB is the height of the tower and BC is the shadow of the tower on the ground.

• Let the angle of elevation of the tower is α.

• ∵ $\dfrac{height of tower AB}{shadow of tower BC}$ =  $\dfrac{\sqrt{3}}{1}$              (Given)

• Now, in the right angle triangle Δ ABC in the attached figure,

•   tan α =   $\dfrac{perpendicular (AB)}{Base (BC)}$

•   tan α = $\dfrac{\sqrt{3}}{1}$

•  ∴ tan α = tan 60°               (∵ tan 60° = √3 )

 ∴       α  =  60° .

Answer 2

Answer:

Let height of a tower, AB = √3  

length of its shadow , BC = 1 

Let angle of elevation of the Sun is θ .

In right angle ∆ ABC , 

⇒ tan θ = P/B 

⇒ tan θ  = AB/BC

⇒ tan θ  = √3/1

⇒ tan θ  = √3 

⇒ tan θ  = tan 60° [tan 60° = √3]

⇒ θ = 60°