Question

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.) 12. 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 form similar triangles (same - angle situation, so the ratios of height to shadow length are equal). Let the height of the tree be \(h\). The ratio for the person is \(\frac{6}{3}\), and for the tree is \(\frac{h}{15}\). So we have the proportion \(\frac{6}{3}=\frac{h}{15}\).

Step2: Solve the proportion

Cross - multiply: \(3h = 6\times15\). Then \(3h=90\). Divide both sides by 3: \(h=\frac{90}{3}\).

Answer:

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