Question

solve each problem. show your work.

1. a 5-ft-tall boy casts a shadow that is 4 ft long. at the same time, a big tree casts a shadow that is 16 ft long. what is the height of the tree?
2. a 2-ft-tall child casts a shadow that is 8 ft long. at the same time, a tree casts a shadow 32 ft long. how tall is the tree?
3. a 6-ft-tall man casts a shadow that is about 10 ft long. at the same time, a building casts a shadow 60 ft long. how tall is the building?
4. a tower casts a shadow that is about 210 m long. at the same time, a 4-m post casts a shadow 8 m long. what is the height of the tower?

Explanation:

Problem 1:

Step1: Set up proportion

Let \( h \) be the height of the tree. The ratio of height to shadow length should be equal. So, \(\frac{5}{4}=\frac{h}{16}\).

Step2: Solve for \( h \)

Cross - multiply: \( 4h = 5\times16 \). Then \( 4h=80 \), divide both sides by 4: \( h = 20 \).

Step1: Set up proportion

Let \( h \) be the height of the tree. The proportion is \(\frac{2}{8}=\frac{h}{32}\).

Step2: Solve for \( h \)

Cross - multiply: \( 8h=2\times32 \). So \( 8h = 64 \), divide by 8: \( h = 8 \).

Step1: Set up proportion

Let \( h \) be the height of the building. The proportion is \(\frac{6}{10}=\frac{h}{60}\).

Step2: Solve for \( h \)

Cross - multiply: \( 10h=6\times60 \). Then \( 10h = 360 \), divide by 10: \( h = 36 \).

Answer:

The height of the tree is \( 20 \) ft.

Problem 2: