157. A girl 1.6 m tall stands 7.2 m from a lamp at night. Her shadow from the light is 1.8 long. Find the height of the lamp post.

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UpStudy AI · Accepted Answer

Let the height of the lamp post be $$ L $$. The tip of the girl's shadow is at a distance of

$$
7.2\,\text{m} + 1.8\,\text{m} = 9.0\,\text{m}
$$

from the lamp.

Because the lamp, the top of the lamp, and the tip of the shadow form a triangle that is similar to the triangle formed by the girl, the top of her head, and the tip of her shadow, we can set up the proportion

$$
\frac{L}{9.0} = \frac{1.6}{1.8}
$$

Solving for $$ L $$:

$$
L = 9.0 \times \frac{1.6}{1.8}
$$

Simplify the fraction:

$$
\frac{1.6}{1.8} = \frac{16}{18} = \frac{8}{9}
$$

Then,

$$
L = 9.0 \times \frac{8}{9} = 8.0
$$

Thus, the height of the lamp post is $$ 8\,\text{m} $$.
The lamp post is 8 meters tall.

A girl 1.6 m tall stands 7.2 m from a lamp
at night. Her shadow from the light is 1.8
long. Find the height of the lamp post.

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