Question

lesson 2 - 8
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?

1. in the figure, the triangles are similar. what is the distance d across the pond?
2. on a golf course, a flagstick casts a 150 - inch shadow at the

same time that a nearby tee casts a 5 - inch shadow. if the
toe is ( 2 \frac { 3 } { 4 } ) inches tall, how tall is the flagstick?

1. in the figure, the triangles are similar. what is the distance d from the

senior high to the junior high? round to the nearest tenth.

Explanation:

Step1: Set up proportion

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

Step2: Cross - multiply

Cross - multiplying gives \(7h = 4.5\times17.5\).

Step3: Calculate the right - hand side

\(4.5\times17.5=78.75\). So \(7h = 78.75\).

Step4: Solve for \(h\)

Divide both sides by \(7\), \(h=\frac{78.75}{7}=11.25\) feet.

Answer:

The lamppost is \(11.25\) feet tall.