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Q. A vertical pole of length 6m casts a shadow 4m long on the

ground and at the, same time a tower casts a shadow 28m

Find the height of the tower.

Sol:

AB represents the tower

PQ represents the pole

BC represents the shadow of the tower

QR represents the shadow of the pole

Ιn ΔPQR and ΔABC,

∠PQR

=

∠ABC

.....[each is 90^o]

∠PRQ

=

∠ACB

.....[Sun’s altitude at the same time]

∴

ΔPQR

~

ΔABC

.....[by AA similarity ]

PQ

AB

=

QR

BC

.....[corresponding sides of similar triangles]

6

AB

=

4

28

∴

AB

=

42m

∴

Height of the tower is

42m

7

6

AB

=

1

7

AB

=

7

×

6

A vertical pole of length 6m

6m

casts a shadow 4m

tower

casts a shadow 28m

28m

P

Q

R

A

B

C

4m