Question

If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is
A. 1.5 m
B. 2 m
C. 2.5 m
D. 2.8 m

Answer 1

a 1.5 m tall girl stands at a distance 3 m from a lamp post and casts a shadow of length 4.5 m on the ground then following figure can be drawn( please see in attachment)

• let height of girl is AB = 1.5 m

• height of lamp-post be DC

• length of girl's shadow  AE = 4.5 m

• from figure:

         in triangle BAC

         tan ∅ = 1.5/4.5 = 1/3

         in triangle DCE

         tan ∅ = DC / (4.5 + 3) = DC / 7.5

         as tan ∅ is equal in both case therefore

         1.5/4.5 = DC/7.5

         1/3 = DC/7.5

         DC = 2.5

therefore height of lamp-post is 2.5 m

Answer 2

Option C: The height of the lamp - post is 2.5 m

Explanation:

Given that a girl is 1.5 m tall stands at a distance of 3 m from a lamp - post and casts a shadow of length 4.5 m on the ground.

We need to determine the height of the lamp - post.

The image of the figure containing these measurements is attached below:

From the figure, we have,

$BD=3$, $DE=4.5$ and $CD=1.5$

Let us consider the triangle CDE,

$\tan \theta=\frac{C D}{D E}$

Substituting the values, we have,

$\tan \theta=\frac{1.5}{4.5}$  ------------(1)

Let us consider the triangle ABE,

$\tan \theta=\frac{A B}{B E}$

Substituting the values, we have,

$\tan \theta=\frac{A B}{3+4.5}$

$\tan \theta=\frac{A B}{7.5}$  --------------(2)

From (1) and (2), we have,

$\frac{1.5}{4.5}=\frac{A B}{7.5}$

Multiplying both sides by 7.5, we get,

$\frac{11.5}{4.5}={A B}$

Dividing, we get,

$2.5=AB$

Thus, the height of the lamp - post is 2.5 m

Therefore, Option C is the correct answer.

Learn more:

(1) A 1.5m tall boy stands at a distance of 3m from a lamp post and casts a shadow of 4.5m on the ground.find the height of lamp post by trignometric ratios

brainly.in/question/281672

(2) A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 metre per second. if the lamp is 3.6 m above the ground. find the length of eyeshadow after 4 seconds.

brainly.in/question/5362064