Question

Harmeet is 6 feet tall and casts a shadow of 3 feet long. What is the height of a nearby pole if it casts a shadow of 12 feet long at the same time?

Answer 1

Harmeet and the pole will be perpendicular to the ground.
So, PQ || ST
In ΔPQR and ΔSTR,
∠PQR = ∠STR    ...(Both are right angles)
∠PRQ = ∠SRT    ...(common angle)
ΔPQR and ΔSTR  ...(AA crriterion for similarity)

`"PQ"/"ST" = "QR"/"TR"`

⇒ `"h"/(6) = (12)/(3)`
⇒ h = 24 feet
Hence, the height of the pole is 24 feet.