Trigonometry/Cal

Question

A ship is headed due north at a constant 14 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 12 miles per hour, in what direction are the currents running?

Answer 1

Draw a sketch with ship's velocity 14 along y-axis, and current 12 with large negative y and a small positive x in order to produce a 15° deviation from North for the resultant vector, which is 75° from positive x-axis (I wasted much time before realizing this simple fact!). So tan 75° = (14+y)/x = 3.73.. and y ≅ 3.73•x - 14. We also know that x² + y² = 144. Combining these gives 14.93•x² - 104.5•x + 52 = 0, whose lesser solution is x = 0.539. Then y = -11.99, angle = tan^-1 (-11.99/0.539) = -87.4°. The current is running just 2.6° East of South.