pole of length 6 m casts a shadow 4 m 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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Answer:
Correct Question:
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Solution:
Given,
Length of the vertical pole = 6 m
Shadow of the pole = 4 m
Let the height of the tower be h m.
Length of the shadow of the tower = 28 m
Now,
In ΔABC and ΔDFE,
∠C = ∠E (angle of elevation)
∠B = ∠F = 90°
By AA similarity criterion,
ΔABC ~ ΔDFE
We know that the corresponding sides of two similar triangles are proportional.
AB/DF = BC/EF
6/h = 4/28
h = (6 ×28)/4
h = 6 × 7
h = 72
Hence, the height of the tower = 42 m.
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