Question

A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50 m long on the ground. The height of the tower is
(a) 100 m
(b) 120 m
(c) 25 m
(d) 200 m

Answer 1

Answer:

The height of the vertical tower is 100 m.

Among the given options option (a) 100 m is the correct answer.

Step-by-step explanation:

Let AB be a vertical stick and AC be a Shadow of a stick . DE be the vertical tower and DF be it's shadow

Given :  

AB = 20 m

DF = 50 m

AC = 10 m

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 ∆ ABC &  ∆DEF

∠DFE = ∠BCA   (sun makes equal angles with the ground)

∠A = ∠D     (each 90°)

Therefore ∆ ABC ~ ∆DEF (By AA similarity)

AB/DE = AC/DF

[Since corresponding sides of two similar triangles are proportional]

20/DE = 10/50

20/DE = ⅕

DE = 20 × 5  

DE = 100 m  

Hence, the height of the vertical tower is 100 m.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Answer:

Let the height of the tower be x metres

IMAGINE,

Since the two triangles are similar by AA similarity criterion, we have

Step-by-step explanation:  x/50 = 20/10

on cross multiplication :

x = 2 * 50 =  100m

hope this helps you!!!!