Calculating Caleb's Angle on Circular Ski Trail
How can we calculate the angle that Caleb has moved through on the circular ski trail?
Given that Caleb is skiing on a circular ski trail with a radius of 0.7 km, starting at the 3-o'clock position and travelling 2.4 km in a counterclockwise direction.
Calculation of Caleb's Angle
To calculate the angle that Caleb has moved through on the circular ski trail, we need to determine the fraction of the circle he has covered and convert it into degrees.
Firstly, we calculate the circumference of the circular trail using the formula: circumference = 2 * π * radius. With a radius of 0.7 km, the circumference is approximately 4.4 km.
Since Caleb has traveled 2.4 km, we need to find the fraction of the circle he has covered. This can be determined by dividing the distance Caleb traveled (2.4 km) by the circumference of the circle (4.4 km).
After finding the fraction, we convert it into degrees by multiplying it by 360 degrees (a full circle). So, the angle moved through by Caleb is: (2.4/4.4) * 360 = approximately 196 degrees.
Therefore, Caleb has moved through an angle of approximately 196 degrees on the circular ski trail.