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, then find how far she is away from the base of the pole.

Question

Philoid · Accepted Answer

Let P be the position of the street bulb fixed on a pole PQ = 6m.

CD = 1.5 m be the height of a woman

ED = 3 m. (Shadow of women)

Let distance between pole and woman be x meter.

Here, woman and pole both are standing vertically.

So,

CD || PQ

In ∆CDE and ∆PQE,

∠E [common angle]

∠PQE = ∠CDE [each equal to 90°]

∴ ∆CDE ∼ ∆PQE [by AAA similarity criterion]

Then,

Hence,

She is at the distance of 9 m from the base of the pole.