Question

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a shadow 30 m long. Determine the height of the tower.

Answer 1

SOLUTION :  

Let AB be a tower and CD be a stick.

Given : CD = 10 cm

Shadow of AB is BE = 30 m

Shadow of CD is DF = 8 cm

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 /10 = 30/8

AB = 30 m ×10 cm / 8cm

AB = (30 × 5)/4

AB = 15 ×5 /2

AB = 75/2

AB = 37.5 m

Hence, the height of the tower is 37.5 m.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi , friend !!

here is your answer !!!

Length of stick = 10cm

shodow length = 8cm


length of tower be X


length of Shadow = 30



using property of similar ∆


we get ,

length of tower be =>

30× 10 / 8

=> 37.5 cm


hope it help you !!!

thanks !!

Ranjankumar