Robin rides a personal watercraft 75° west of south at 70 miles/hour. the water current is moving 6 miles/hour at an angle of 75° south of west. what is the actual speed (rounded to the nearest hundredth) of robin's watercraft?
a.
71.19 miles/hour
b.
73.19 miles/hour
c.
75.12 miles/hour
d.
77.13 miles/hour

B. 73.19 mi/hr

Step-by-step explanation:

First we need to define the angles from a common reference.  Robin's watercraft is moving 75° west of south, which is the same as 15° south of west.  The river is flowing at 75° south of west.

The watercraft velocity relative to the water is:

wx = 70 cos 15° ≈ 67.615

wy = 70 sin 15° ≈ 18.117

The river's velocity is:

rx = 6 cos 75° ≈ 1.553

ry = 6 sin 75° ≈ 5.796

Robin's net velocity is:

vx = wx + rx ≈ 69.168

vy = wy + ry ≈ 23.913

The speed (magnitude of velocity) is:

v = √(vx² + vy²)

v ≈ √(69.168² + 23.913²)

v ≈ 73.19