Question

A girl 160 cm tall, stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?

Answer 1

To find the height of the lamp post using similar triangles, we can set up a proportion based on the girl and her shadow.

Let:
- \( h \) be the height of the lamp post.
- The height of the girl is 160 cm.
- The distance from the base of the lamp post to the girl is 360 cm.
- The length of the girl's shadow is 90 cm.

We can form two similar triangles:
1. The triangle formed by the lamp post, the ground, and the tip of the shadow of the girl.
2. The triangle formed by the girl, the ground, and the tip of her shadow.

Using the similar triangles, we can set up the following proportion:

\[
\frac{h}{360} = \frac{160}{90}
\]

Now, we can cross-multiply to solve for \( h \):

\[
h \cdot 90 = 160 \cdot 360
\]

Calculating \( 160 \cdot 360 \):

\[
160 \cdot 360 = 57600
\]

Now, we can write the equation as:

\[
90h = 57600
\]

Solving for \( h \):

\[
h = \frac{57600}{90} = 640
\]

Thus, the height of the lamp post is \( \boxed{640} \) cm.