A vertical pole of a length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

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Length of the vertical pole = 6m (Given)
Length of the shadow of the pole = 4 m (Given)
Let Height of tower = h m
Length of shadow of the tower = 28 m (Given)
In ΔABC and ΔDEF,
∠C=∠E(angular elevation)
∠B=∠F=90∘
∴ΔABC∼ΔDFE (By AAA similarity criterion)
∴ABDF=BCEF (If two triangles are similar then their corresponding sides are proportional.)
∴6h=428
⇒h=6×284
⇒h=6×7
⇒h=42m
Hence, the height of the tower is 42 m.

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