Your calculator is set to compute the cosine of angles measured in radians instead of degrees. Indeed, 3^2 + 5^2 = 34, and cos 65 > 0, so 3^2 + 5^2 - 2 x 3x5 cos 65 cannot be 50.8.
Marie is training for the Marathon. From her home, she runs 5 km south west. She then changes direction and run 3 km N 20 W to get to the park.
a) how far and what direction is the park from Marie's home?
R^2 = 3^2 + 5^2 - 2 x 3x5 cos 65
R^2 = 50.8
R = 7.12
In my textbook the R = 4.6. What am I doing wrong?