Applying the law of cosines to a triangle to find the missing length

The video tutorial explains a geometry problem involving points on the shoreline of Lake George. The teacher guides through the process of analyzing the triangle formed by these points, discussing why certain formulas like the Pythagorean theorem and trigonometric functions are not applicable. The focus is on using the law of cosines to calculate the distance between two points, A and B, given the distances from a third point, C, and the angle at C. The tutorial concludes with the calculation of the distance, ensuring the result is reasonable within the context of the problem.

Identify the values used in the law of cosines formula for this problem.

What is the final calculated distance from A to B, and does it seem reasonable in the context of the problem?

What steps did the teacher take to ensure the calculations were correct?