Question

a tower of height 24m casts a shadow 50m and at same time a girl of height 1.8m casts a shadow find the length of the shadow of the girl​

Answer 1

Given:

Height of the tower = 24 m

Height of the girl = 1.8 m

The length of the shadow cast by the tower = 50 m

To find:

The length of the shadow of the girl

Solution:

From the figure attached below we have,

AB = height of the tower  = 24 m

BE = shadow cast by the tower  = 50 m

DE = shadow cast by the girl

CD = height of the girl = 1.8 m

Consider ΔABE & ΔCDE, we have

∠E = ∠E ...... (common angle)

∠ABE = ∠CDE = 90° ...... (both the tower and the man stand vertical)

∴ ΔABE ~ ΔCDE ...... by AA similarity

We know that the corresponding sides of two similar triangles are proportional to each other

∴   $\frac{AB}{CD} = \frac{BE}{DE}$

now, substituting the values of BE = 50 m, AB = 24 m & CD = 1.8 m

⇒   $\frac{24}{1.8} = \frac{50}{DE}$

⇒   $DE = \frac{50\:\times\:1.8}{24}$

⇒ DE = 3.75 m  

Thus, the length of the shadow of the girl is 3.75 m.

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Also View:

The length of the shadow of a post becomes 3 CM smaller when the angle of elevation of the sun increases from 45 degree to 60 degree find the height of the post.

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A boy of height 1.75m is walking away from the base of a lamp post at a speed of 1.2m/s . If the lamp is 7m above the ground , then find the lenght of the shadow after 5sec.

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Answer 2

Answer:

3.75 m

Step-by-step explanation:

the length of the shadow of the girl is "3.75 metre"

hope it helps you guy!!!!!!!!!