Circle Geometry and Angle Conversions

The video tutorial explains how to find the angle in degrees that subtends an arc length of 10 centimeters on a circle with a radius of 4 centimeters. It introduces the arc length formula, s = rθ, where s is the arc length, r is the radius, and θ is the angle in radians. By substituting the given values, the angle θ is calculated in radians and then converted to degrees using the conversion factor 180/π. The final result is approximately 143.24 degrees.

What is the radius of the circle given in the problem?

• 2 cm

• 4 cm

• 8 cm

• 6 cm

Tags

CCSS.HSG.C.B.5

What is the length of the arc mentioned in the problem?

• 10 cm

• 8 cm

• 12 cm

• 5 cm

Tags

CCSS.HSG.C.B.5

In the formula s = rθ, what does 's' represent?

• Radius

• Angle in degrees

• Arc length

• Diameter

Tags

CCSS.HSG.C.B.5

What is the unit of the angle θ in the formula s = rθ?

• Degrees

• Radians

• Gradians

• Turns

Tags

CCSS.HSG.SRT.C.8

After substituting the given values, what equation do we get?

• 10 = 4θ

• 10 = 2θ

• 8 = 4θ

• 12 = 4θ

Tags

CCSS.HSF.TF.B.7

What is the value of θ in radians after solving the equation?

• 4.5

• 1.5

• 2.5

• 3.5

Tags

CCSS.HSF.TF.A.1

What is the conversion factor from radians to degrees?

• 90/π

• 270/π

• 360/π

• 180/π

Tags

CCSS.HSF.TF.A.1

What is the approximate angle in degrees after conversion?

• 143.24 degrees

• 150.12 degrees

• 120.45 degrees

• 130.34 degrees

Tags

CCSS.HSG.C.B.5

Why do we need a decimal approximation for the angle in degrees?

• Because the angle is too small

• Because the radius is large

• Because the arc length is unknown

• Because π is an irrational number

Tags

CCSS.4.MD.C.6

What is the final step in finding the angle in degrees?

• Using a calculator

• Using a protractor

• Using a ruler

• Using a compass

Tags

CCSS.4.MD.C.6