Question

A golfer takes two strokes to putt a golf ball into a hole. On the first stroke, the ball moves 4.0m at an angle 60◦ East of North. On the second, it moves 3.0m at an angle 70◦ South of East. If the golfer had instead hit the ball directly into the hole on the first stroke, what would have been the magnitude and direction of the ball’s displacement

Answer 1

sketch it. labale the angles, You have a SAS triangle. You want the third side:
law of cosines
c^2=a^2+b^2 -2ab*cosC
you know, a, b, and angle C

Answer 2

All angles are measured CCW from +x-axis.
Disp. = 4m[30o] + 3[290].
X = 4*Cos30 + 3*Cos290 = 4.49 km.
Y = 4*sin30 + 3*sin290 = -0.82km.

x + yi = 4.49 - 0.82i = 4.56km[-10.3] =
4.56km[10.3o]S. of E.