Question

lesson 9.12
solve each problem. be sure to write an equation.
show your work.

1. a 6-ft-tall boy casts a shadow 3 ft long. at the

same time, a flagpole casts a shadow 12 ft long.
how tall is the flagpole?

1. a 3-ft-tall girl standing near a tree casts a

shadow 10 ft long. at the same time, a tree
casts a shadow 40 ft long. how tall is the tree?

1. a 6-ft-tall man casts a shadow that is about 5 ft

long. at the same time, a building casts a
shadow 60 ft long. how tall is the building?

1. a tower casts a shadow that is about 18 m

long. at the same time, a 3-m post casts a
shadow 0.6 m long. what is the height of
the tower?

Explanation:

Problem 1:

Step1: Define variables and set up proportion

Let \( h \) be the height of the flagpole. Since the ratios of height to shadow length are equal (similar triangles), we have \(\frac{6}{3}=\frac{h}{12}\).

Step2: Solve for \( h \)

Cross - multiply: \( 3h = 6\times12 \). Then \( 3h=72 \). Divide both sides by 3: \( h=\frac{72}{3}=24 \).

Step1: Define variables and set up proportion

Let \( t \) be the height of the tree. The proportion is \(\frac{3}{10}=\frac{t}{40}\).

Step2: Solve for \( t \)

Cross - multiply: \( 10t = 3\times40 \). So \( 10t = 120 \). Divide both sides by 10: \( t=\frac{120}{10}=12 \).

Step1: Define variables and set up proportion

Let \( b \) be the height of the building. The proportion is \(\frac{6}{5}=\frac{b}{60}\).

Step2: Solve for \( b \)

Cross - multiply: \( 5b=6\times60 \). Then \( 5b = 360 \). Divide both sides by 5: \( b=\frac{360}{5}=72 \).

Answer:

The flagpole is 24 ft tall.

Problem 2: