What direction in degrees are the currents running?

Question

A ship is headed due north at a constant 18 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 16 miles per hour, in what direction are the currents running? (Enter your answers as a comma-separated list. Round your answers to the nearest whole number.)

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Answer 1

We have a triangle with sides of length 18 and 16, and an angle of 15° - 0° = 15° opposite the 16. Then, the angle opposite the 18 will be found using the sin law.

sin x/18 = sin 15º/16

Then, x = sin^-1 (18/16 sin 15º) = 16.9281005893827º or 180º-16.9281005893827º

Note that this is the internal angle, so 180º minus this will be the amount to subtract from 15º to show the direction in the reverse direction of the current, so the current will be 180º + this.

Then, 180º + 15º - (180º-16.9281005893827º) = 31.9281005893827º (This angle makes sense, because the speed of the ship is just slightly more than the current, so the 15° angle is slightly closer to 0° than 31.9281005893827º).

180º + 15º - (16.9281005893827º)) =178.071899410617 °

(32,178)