Problem: 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?

## Step 1: Understand the Problem<br />### The problem involves similar triangles formed by the girl and her shadow, and the lamp post with its light casting a shadow. We need to find the height of the lamp post using these proportions.<br /><br />## Step 2: Set Up Proportions<br />### The girl's height and her shadow form one triangle, while the lamp post and the total distance from the lamp post to the end of the shadow form another similar triangle. Let $h$ be the height of the lamp post. The proportion is given by:<br />\[<br />\frac{160}{90} = \frac{h}{360 + 90}<br />\]<br /><br />## Step 3: Solve for the Height of the Lamp Post<br />### Simplify and solve the equation for $h$:<br />\[<br />\frac{160}{90} = \frac{h}{450}<br />\]<br />Cross-multiply to get:<br />\[<br />160 \times 450 = 90 \times h<br />\]<br />Calculate:<br />\[<br />72000 = 90h<br />\]<br />Divide both sides by 90:<br />\[<br />h = \frac{72000}{90} = 800<br />\]