Optimistic Outlook on Skiing Adventure

To find the angle that Stephen skis on a circular trail, we can use the formula for the length of an arc of a circle. The length of the arc is equal to the radius of the circle multiplied by the angle in radians.

Stephen is skiing on a circular ski trail with a radius of 0.9 km. He starts at the 3 o'clock position, which is the easternmost point on the trail, and travels 2.35 km in a counterclockwise direction.

In this scenario, we can calculate the angle that Stephen skis by using the formula for the length of an arc of a circle. The formula is:

Length of Arc = Radius x Angle (in radians)

Given that the radius is 0.9 km and the length of the arc (path Stephen skis) is 2.35 km, we can calculate the angle as follows:

Angle = 2.35 km / 0.9 km = 2.6111 radians

Therefore, the angle that Stephen skis on the circular trail is approximately 2.6111 radians. This calculation helps us understand the path he takes during his skiing adventure.