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A man 1.8 m high stands at a distance of 3.6 m from a lamp pos

Question

A man 1.8 m high stands at a distance of 3.6 m from a lamp post and casts a shadow of 5.4 m. on the ground. Find the height of the lamp post.

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Text solutionVerified

PQ be the height of lamp post , RS be height of

man and QS be the distance of man

from lamp post and ST br the length of shadow

RS=1.8m QS=3.6m ST=5.4m

now

Δ PQT an d Δ RST

we have

∠ PQT = ∠ RST = 9 0^{\circ}

∠ PTQ = ∠ RTS [co mm o n]

∴ Δ PQT ≅ Δ RST [A . A]

now

\frac{PQ}{RS} = \frac{QT}{ST}

\frac{PQ}{1.8} = \frac{QS + ST}{ST} = \frac{3.6 + 4.4}{5.4}

PQ = \frac{9.6}{360} = 3 m

[PQ=3m]

∴

height of lamp post is 3 m.

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Question Text	A man 1.8 m high stands at a distance of 3.6 m from a lamp post and casts a shadow of 5.4 m. on the ground. Find the height of the lamp post.
Answer Type	Text solution:1
Upvotes	150