Question

1. in the diagram, the vertical lines are parallel.

name all pairs of similar triangles.

1. connecting to real life a map shows the number

of steps you must take to get to a treasure. however, the
map is old, and the last dimension is unreadable. how
many steps do you need to take from the pyramids to the
treasure? (see example 3.)

1. smp.4 a person who is 6 feet tall casts a 3-foot-long

shadow. a nearby pine tree casts a 15-foot-long
shadow. draw a diagram of the situation. what is the
height h of the pine tree?

Explanation:

Step1: Set up proportion

Since the person and the tree with their shadows form similar triangles. Let the height of the tree be \(h\). The proportion is \(\frac{\text{height of person}}{\text{length of person's shadow}}=\frac{\text{height of tree}}{\text{length of tree's shadow}}\).

Step2: Substitute values

We know the person's height is \(6\) feet, person's shadow is \(3\) feet, and tree's shadow is \(15\) feet. So \(\frac{6}{3}=\frac{h}{15}\).

Step3: Solve for \(h\)

Cross - multiply: \(3h = 6\times15\). Then \(3h=90\), and \(h=\frac{90}{3}=30\).

Answer:

The height \(h\) of the pine tree is \(30\) feet.