Question

additional practice

1. at the same time that a 4.5 - foot - tall trash bin casts a 7 - foot shadow,

a nearby lamppost casts a 17.5 - foot shadow. how
tall is the lamppost?

Explanation:

Step1: Set up the proportion

Since the objects and their shadows form similar triangles, we can set up the proportion \(\frac{\text{height of trash bin}}{\text{length of trash bin's shadow}}=\frac{\text{height of lamppost}}{\text{length of lamppost's shadow}}\). Let \(h\) be the height of the lamppost. So, \(\frac{4.5}{7}=\frac{h}{17.5}\).

Step2: Solve the proportion for \(h\)

Cross - multiply: \(7h = 4.5\times17.5\). First, calculate \(4.5\times17.5=78.75\). Then, \(h=\frac{78.75}{7}\). \(h = 11.25\).

Answer:

The lamppost is \(11.25\) feet tall.