Question

A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.

Answer 1

Let A be the position of the street bulb fixed on a pole AB = 6 m and CD = 1.5 m be the height of a woman and her shadow be ED = 3 m.

Let distance between pole and woman be x m.

Here, woman and pole both are standing vertically.

So, CD || AB

In ΔCDE and ΔABE,

∠E = ∠E   ...[Common angle]

∠ABE = ∠CDE   ...[Each equal to 90°]

∴ ΔCDE ∼ ΔABE   ...[By AAA similarity criterion]

Then, `("ED")/("EB") = ("CD")/("AB")`

⇒ `3/(3 + x) = 1.5/6`

⇒ 3 × 6 = 1.5(3 + x)

⇒ 18 = 1.5 × 3 + 1.5x

⇒ 1.5 = 18 – 4.5

∴ x = `(13.5)/1.5` = 9 m

Hence, she is at the distance of 9 m from the base of the pole.