Question

Two ships leave the same port at the same time. One ship sails on a course of 110 degree at 32 mi/h. The other sails on a course of 230 degree at 40 mi/h. Find the distance between them after 2 hours. Express your answer to the nearest mile.

Answer 1

both start at origin
Ship one
110 from north is 20 degrees below +x axis
x1 = 2 * 32 * cos 20
y1 = -2 * 32 * sin 20
Ship 2
230 from north is 40 deg below -x axis
x2 = -2 * 40 cos 40
y2 = -2 * 40 sin 40

d = sqrt [(x2-x1)^2 + (y2-y1)^2 ]

Answer 2

or, since the angle between their travel is 120° use the law of cosines to find the 3rd side of the triangle:

d^2 = 64^2 + 80^2 - 2*64*80 cos 120°