What is the degree measure of an arc 4 ft. long in a circle of radius 10 ft.? 72° 60° 57.6°

Measure of an arc = ( intercepted angle/ full circle) x circumference

4 ft =( intercepted angle/360) x (2 x 10 x pi)

4 = intercepted angle /360 x 62.8

Divide both sides by 62.8

4/62.8 = intercepted angle/360

Multiply both sides by 360

Intercepted angle = (4/62.8) x 360

Angle = 22.93 degrees

22.9 degrees

Step-by-step explanation:

The degree measure (in radians) can be found using the following formula.

Θ=S/r

where S is the arc length and r is the radius.

We know the arc length is 4 feet and the radius is 10 feet. Substitute the values into the formula.

Θ= 4/10

Θ= 0.4

The measure is 0.4 radians.

Convert radians to degrees using the following formula.

Θ * 180/π

We know that Θ= 0.4 , so we can substitute it in.

0.4 * 180/π

0.4 * 57.2957795

22.9183118

Round to the nearest tenth. The 1 in the hundredth place tells us to leave the 9 in the tenth place.

22.9

The angle measure is about 22.9 degrees.

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