Question

a man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2 the height of man is 2m. it is noticed than shadow of the man with respect to first lamp post just touches the foot of second lamp post if the distance between the post is 30m. find the height of the first post

Answer 1

Given:

The height of the man = 2 m

A man is standing between two lamp posts on a horizontal line dividing the distance between them in the ratio 1:2

The distance between the two lamp post is 30 m

The shadow of the man with respect to the first lamp post just touches the foot of the second lamp post

To find:

The height of the first post

Solution:

Referring to the figure attached below, we have

AB = height of the lamp post 1

BE = 30 m = distance between the two lamp post

CD = 2 m = height of the man

Since the divides, the horizontal line dividing the distance between the lamp post 1 and 2 in the ratio of 1:2 and also BE = 30 m

So, let's assume BD = x and DE = 2 x

∴ BD + DE = BE

⇒ x + 2x = 30

⇒ 3x = 30

⇒ x = $\frac{30}{3}$

⇒ x = 10 m

∴ DE = 2x = 2 × 10 = 20 m

Now, consider ΔABE and ΔCDE, we have

∠E = ∠E ....... [common angle]

∠ABE = CDE = 90° ..... [both lamp and man stands vertical on the horizontal line]

∴ ΔABE ~ ΔCDE ...... [by AA similarity]

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

∴ $\frac{AB}{CD} = \frac{BE}{DE}$

substituting CD = 2, BE = 30 & DE = 20

$\implies \frac{AB}{2} = \frac{30}{20}$

$\implies \frac{AB}{2} = \frac{3}{2}$

$\implies \bold{AB = 3\:m}$

Thus, the height of the first lamp post is 3 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

Step-by-step explanation:

answer for this question is 3 m