# Lesson 5 Moving Shadows Practice Understanding

Conestoga wagons in the 1800s had wheels that were smaller in the front than in the back. The front wheels had

(For these problems, disregard the hub at the center of the wheel. Assume the spokes meet in the center at a point. Leave

### 1.

Find the area and the circumference of each wheel.

#### a.

Front-wheel area:

#### b.

Front-wheel circumference:

#### c.

Rear-wheel area:

#### d.

Rear-wheel circumference:

### 2.

Determine the central angle between the spokes on each wheel.

#### a.

Front wheel:

#### b.

Rear wheel:

### 3.

Find the distance on the circumference between two consecutive spokes for each wheel.

#### a.

Front wheel:

#### b.

Rear wheel:

### 4.

The wagons could cover a distance of

### 5.

A wheel rotates

A right triangle has been drawn from a point on a circle centered at

Write the value of

as defined in today’s task. (You will need to find the radius.) Use right angle trigonometry to solve for angle

inside the triangle. Use the measure of

to find (the angle of rotation).

### 6.

### 7.

### 8.

### 9.

### 10.

### 11.

### 12.

In each graph, the angle of rotation is indicated by an arc and

### 13.

What do you notice about the

### 14.

In the graph, the radius of the circle is

Perform the indicated operation and divide out any common factors in your answers.