Arc Length and Angle Calculations

This video tutorial explains how to solve arc length word problems using the formula 2πRθ/360. It covers three examples: a robotic arm, a pleated fan, and a clock's minute hand. Each example demonstrates how to calculate arc length using degrees and radians, and how to apply the formula to real-world scenarios. The video emphasizes the importance of understanding the relationship between degrees, radians, and arc length, and provides step-by-step calculations for each example.

What is the formula for calculating arc length?

• 2πrθ/360

• πr²

• 2πr

• rθ

In the arc length formula, what does θ represent?

• The diameter of the circle

• The angle in degrees or radians

• The radius of the circle

• The circumference of the circle

How many degrees does a robotic arm traverse in one minute if it completes a revolution in two minutes?

• 270 degrees

• 90 degrees

• 360 degrees

• 180 degrees

If a robotic arm moves 270 degrees in 1.5 minutes, how many radians is this equivalent to?

• 3π/2 radians

• π radians

• 2π radians

• π/2 radians

What is the radius of the pleated fan used in the example?

• 5 inches

• 8 inches

• 6 inches

• 7 inches

What angle does the pleated fan sweep when fully open?

• 60 degrees

• 70 degrees

• 80 degrees

• 90 degrees

Using the arc length formula, what is the length of the trim on the pleated fan?

• 8.5 inches

• 9.8 inches

• 10.2 inches

• 11.5 inches

What is the length of the minute hand on the clock in the example?

• 3 inches

• 4 inches

• 5 inches

• 6 inches

How many degrees does the minute hand move in 15 minutes?

• 150 degrees

• 60 degrees

• 90 degrees

• 120 degrees

What is the total angle in degrees that the minute hand moves from 5:12 p.m. to 6:27 p.m.?

• 360 degrees

• 450 degrees

• 540 degrees

• 630 degrees