To find the length of an arc, we use the formula:
Arc length = (angle/360) x (2πr)
where "angle" is the central angle of the arc in degrees, "r" is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14.
In this case, we are given that the central angle is 90° and the radius is 10 km. Substituting these values into the formula, we get:
Arc length = (90/360) x (2π × 10)
Arc length = (1/4) x (20π)
Arc length = 5π
Rounding to the nearest tenth and using the approximation π ≈ 3.14, we get:
Arc length ≈ 15.7
Therefore, the length of the arc is approximately 15.7 km.