To solve this problem, we need to apply the Law of Cosines that is used in mathematics to find the length of one side in a triangle using the lengths of the other two sides and the cosine of the included angle.
From the given information in the problem, the distance between Kayla and Jenna is given as 120 feet. However, the problem does not provide the values for the angles from Jenna's location between Kayla and Paige and the angle from Kayla's location between Jenna and Paige.
Here are the steps we would follow to solve this problem if we had the angles:
1. Suppose we denote the angle from Jenna's location between Kayla and Paige as Alpha (α), and the angle from Kayla's location between Jenna and Paige as Beta (β). These angles should be given in degrees.
2. Convert these angles from degrees to radians. In python, we can use the math.radians() function for this conversion.
3. Calculate the distance between Kayla and Paige using the Law of Cosines. According to the Law of Cosines, if we denote the sides of the triangle as a, b, and c, and the angle opposing the side a as A, then the formula for calculating the distance would be: aˆ2 = bˆ2 + cˆ2 - 2bc*cos(A).
Unfortunately, without the values for Alpha and Beta, we can't determine the distance between Kayla and Paige. These angle values are necessary to solve this kind of problem, as they define the exact positions of Kayla, Jenna, and Paige. Without these angles, we have an infinite number of possibilities for the positions of these three people and hence the distance between Kayla and Paige. On a side note, ensure that the provided angles do not result in a non-existing triangle, i.e., the sum of the angles should be exactly 180 degrees.