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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?
Solution
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.
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