Question

A 1.5 m tall boy is looking at the top of a temple which is 30 metre in height from a point at certain distance. The angle of elevation from his eye to the top of the crown of the temple increases from 30° to 60° as he walks towards the temple. Find the distance he walked towards the temple.

Answer 1

Height of the temple = 30 m 

Height of the man = 1.5 m 

Initial distance between the man and temple = d m. say 

Let the distance walked = x m. 

From the figure 

tan 30° = \(\frac{30-1.5}{d}\)

⇒ \(\frac{1}{\sqrt{3}}\) = \(\frac{28.5}{d}\)

∴ d = 28.5 × √3m ………(1) 

Also tan 60° = \(\frac{28.5}{d-x}\)

⇒ √3 = \(\frac{28.5}{d-x}\)

⇒ √3(d-x) = 28.5 

⇒ √3(28.5 × √3-x) = 28.5 

⇒ 28.5 × 3 – √3x = 28.5 

⇒ √3x = 3 × 28.5-28.5 

⇒ √3x = 2 × 28.5 = 57 

∴ x = \(\frac{57}{\sqrt{3}}\) = \(\frac{19\times3}{\sqrt{3}}\) = 19√3 

= 19 × 1.732 

= 32.908 m. 

∴ Distance walked = 32.908 m.