Exploring Arc Length Calculations

What is the formula for calculating the arc length of a circle?

• s = r * theta

• s = r / theta

• s = r - theta

• s = r + theta

Why is it necessary to use radians in the formula for arc length?

• Radians simplify the calculation.

• The formula only works with radians.

• Degrees are not precise enough.

• Radians are easier to convert.

How do you find the radian measure of a central angle given the arc length and radius?

• Multiply arc length by radius.

• Divide arc length by radius.

• Add arc length to radius.

• Subtract arc length from radius.

What is the result of calculating the arc length when the radius is 9 feet and the central angle is pi/3 radians?

• 9 pi feet

• 3 pi feet

• 6 pi feet

• 27 feet

How do you convert a central angle from degrees to radians for the formula?

• Multiply by 180/pi

• Divide by pi/180

• Multiply by pi/180

• No conversion needed

What is the formula to find the radius of a circle given the arc length and central angle?

• r = s - theta

• r = s * theta

• r = s + theta

• r = s / theta

If the arc length is 8 inches and the central angle is 330 degrees, what is the radius in inches?

• 2.778 inches

• 1.389 inches

• 5.556 inches

• 0.694 inches

What is the first step in calculating the distance between two cities on the same longitude?

• Convert their latitudes to radians.

• Determine the central angle between them.

• Calculate the radius of the Earth.

• Find the difference in their latitudes.

How do you convert degrees, minutes, and seconds to radians?

• Only degrees need to be converted using pi/180.

• Divide by 60 and then multiply by pi/180.

• Use the DMS function and multiply by pi/180.

• Add degrees, minutes, and seconds then multiply by pi/180.

What is the approximate distance between two cities if the Earth's radius is 4000 miles and the central angle is 41 degrees?

• Approximately 1000 miles

• Around 591 miles

• Nearly 800 miles

• Close to 450 miles