Final answer:
The measure of the indicated arc length in a circle with a tangent KL can be calculated if the radius of curvature and the central angle A are known, using the provided formulas.
Step-by-step explanation:
The student is asking about the measure of an arc length on a circle where KL is a tangent to the circle. To find the measure of the arc, we need to know the angle subtended by the arc at the center of the circle, designated as A. According to the information provided, the arc length As is found by rotating a radius through an angle A0. The formula for arc length is As = rθ where r is the radius of curvature and θ (theta) is the angle in radians. If the angle is given in degrees, we can use the conversion that the circumference of the circle corresponds to 360 degrees or 2π radians. Thus, for an angle A in degrees, the arc length is given by As = θ2πr( A/360). This relationship allows us to calculate the arc length once we know the radius of the circle and the subtended angle.