Determine the value of a, the arc length in inches intercepted by the angle with a measure of 2.1 radians, given that the radius of the circle is 7 inches.

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 * 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 7 inches

θ = pi/4

2π = 360 degrees

180 degrees = π radians

1 radian = 180/π

2.1 radians = 2.1 * 180/π = 120.38 degrees

Therefore,

Length of arc = 120.38/360 * 2 * 3.14 * 7

Length of arc = 14.7 inches rounded up to 1 decimal places