Question

A man 1.8 m high stands at a distance of 3.6 m from one lamp post and cast a shadow 5.4 m on the ground find the height of the lamp post

Answer 1

SOLUTION

Let,

AB be the height of the lamp post ,CD be the height of the man , BD be the distance of the man from the lamp-post and DE be the length of the shadow.

Here, CD= 1.8 m ,BD = 3.6 m, DE = 5.4 m

Now,

       In triangle ABE and triangle CDE we have,

       ∠ABE = ∠CDE (both 90°)

       ∠AEB = ∠CED (common angle)

∴ΔABE ≈ ΔCDE (A.A)

∴AB/CD = BE/DE

⇒AB/1.8= (BD+DE)/5.4

⇒AB/1.8= (3.6+5.4)/5.4

⇒AB/1.8= 9/5.4

⇒AB= 16.2/5.4

⇒AB= 3m

∴Height of the lamp post=3m.