Question

A vertical stick 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.

Answer 1

SOLUTION :  

Let AB be a tower and CD be a stick.

Given : CD = 6m

Shadow of AB is BE = 28m

Shadow of CD is DF = 4m

Here, stick and tower  both are perpendicular to the ground and they cast Shadow at the same time, so Sun makes equal angles with the ground for both the triangles.

In ∆ ABE ~ ∆CDF

∠DFC = ∠BEA (sun makes equal angles with the ground)

∠CDF = ∠ABE (each 90°)

Therefore ∆ ABE ~ ∆CDF (By AA similarity)

AB/CD = BE/DF

[Since corresponding sides of two similar triangles are proportional]

AB /6 = 28/4

AB = 28 ×6/4

AB = 7 × 6

AB = 42 cm

Hence, the height of the tower is 42 m.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi friend !!!

length of stick = 6m.
shadow length = 4m



length of tower be x


it's shadow is 28

{ using the property of similar ∆ }



now length of tower is


6 × 28 / 4

=> 42 m


hope it helps you !!




thanks !!!

ranjankumar