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.

Question

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.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Geometry Questions