Question

2.
A 1.5 m tall boy is looking at the top of a temple which is 30 meter 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

Answer:

Height of the temple =30m

Height of the man =1.5m

Let initial distance between the man and the temple = d m

Let the distance walked = x m

From the figure

tan30

∘

=

d

30−1.5

⇒

3

1

=

d

28.5

⇒d=28.5×

3

m ........(1)

tan60

∘

=

d−x

28.5

⇒

3

=

d−x

28.5

⇒

3

(d−x)=28.5

⇒

3

(28.5×

3

−x)=28.5 (from (1))

⇒28.5×3−

3

x=28.5

⇒

3

x=3×28.5−28.5=2×28.5=57

⇒

3

x=57⇒x=

3

57

=

3

19×3

=19

3

⇒x=19×1.732=32.908m

∴ Distance walked towards the temple =32.908m