A golfer sees the green (where the hole is) at a distance of 120.0 m at heading 75.0° north of west. She also sees her teammate at a distance of 60.0 m and heading 15.0° north of east.

Question

What distance and direction would her teammate have to land the ball to hit the green?

Answer 1

Magnitude:use Pythagoras theorem (note 90° between the teammate and the green).

Angle (from point of view of teammate)
= atan(120/60)+75° West of south
since the golfer is at 75° west of south from the point of view of the teammate.

Answer 2

d = d2-d1 = 120m[105o]-60m[15o]

X = 120*cos105 - 60*cos15 = -89.0 m.
Y = 120*sin105 - 60*sin15 = 100.4 m.

Tan Ar = Y/X = 100.4/-89.0 = -1.12789
Ar = -48.44o = Reference angle.
A = -48.44 + 180 = 131.6o = Direction.

d = Y/sinA = 100.4/sin131.6 = 134.3 m.
[131.6].