To find the angle that an arc subtends at the center of a circle, we can use the formula:
θ = (s / r) * 180 / π
Where:
θ is the angle in degrees,
s is the length of the arc,
r is the radius of the circle, and
Ï€ is a mathematical constant approximately equal to 3.14159.
Given that the radius (r) of the circle is 10 cm and the length of the arc (s) is also 10 cm, we can substitute these values into the formula:
θ = (10 / 10) * 180 / π
Simplifying this expression:
θ = 1 * 180 / π
To determine the value in degrees, we can substitute the approximate value of π as 3.14159:
θ = 180 / 3.14159
Calculating this expression:
θ ≈ 57.29578 degrees
Therefore, the angle that the given arc subtends at the center of the circle is approximately 57.3 degrees (rounded to the nearest 0.1).