Final answer:
The length of the arc intercepting an angle of 3π/4 radians in a circle with radius 2 is 3π/4 units.
Step-by-step explanation:
The length of an arc in a circle is determined by the degree measure of the central angle it intercepts. In this case, the angle measures 3π/4 radians. To find the length of the arc, we need to know the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius. Given that the radius is 2, we can substitute this value into the formula to find the circumference: C = 2π(2) = 4π.
Since a full revolution around a circle is 2π radians, we can find the length of the arc by setting up a proportion. We have 2π radians correspond to a full circle of length 4π. Therefore, 3π/4 radians will correspond to a length of (3π/4)(4π)/(2π) = 6π/8 = 3π/4 units.