Questions: A snowman casts a shadow that is 8 feet long at the same time a sledding hill casts a shadow that is 32 feet long. If the snowman is 4 feet tall, how tall is the sledding hill?

A snowman casts a shadow that is 8 feet long at the same time a sledding hill casts a shadow that is 32 feet long. If the snowman is 4 feet tall, how tall is the sledding hill?

Transcript text: A snowman casts a shadow that is 8 feet long at the same time a sledding hill casts a shadow that is 32 feet long. If the snowman is 4 feet tall, how tall is the sledding hill?

Solution

Solution Steps

Step 1: Identify the given information

The snowman's height is \( 4 \) feet.
The snowman's shadow is \( 8 \) feet long.
The sledding hill's shadow is \( 32 \) feet long.

Step 2: Set up the proportion

Since the shadows are cast at the same time, the triangles formed by the snowman and the sledding hill are similar. Therefore, the ratio of height to shadow length is the same for both: \[ \frac{\text{Snowman's height}}{\text{Snowman's shadow}} = \frac{\text{Sledding hill's height}}{\text{Sledding hill's shadow}} \] \[ \frac{4}{8} = \frac{h}{32} \]

Step 3: Solve for the sledding hill's height

Cross-multiply to solve for \( h \): \[ 4 \times 32 = 8 \times h \] \[ 128 = 8h \] \[ h = \frac{128}{8} = 16 \]

The sledding hill is \( 16 \) feet tall.