2024_Central Angles and Arc Length Practice

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides are radii that extend to the circumference.

Front

How do you calculate the arc length of a circle?

Back

Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is the relationship between the radius and the arc length?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given central angle.

Front

What is a minor arc?

Back

A minor arc is the shorter arc connecting two points on a circle, measured by the central angle less than 180 degrees.

Front

What is a major arc?

Back

A major arc is the longer arc connecting two points on a circle, measured by the central angle greater than 180 degrees.

Front

If the radius of a circle is 1.5 inches, what is the arc length for a 90-degree angle?

Back

Arc Length = (90/360) * 2π(1.5) = 2.36 inches.

Front

What is the formula for finding the measure of a central angle given the arc length?

Back

Central Angle (θ) = (Arc Length / (2πr)) * 360.

Front

How do you convert arc length to degrees?

Back

Use the formula: Degrees = (Arc Length / (2πr)) * 360.

Front

What is the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

If a jogger runs 230 feet on a circular track with a radius of 140 feet, how do you find the measure of the minor arc?

Back

Use the formula: Central Angle (θ) = (Arc Length / (2πr)) * 360. Plug in the values to find θ.