Trig Problem (pls help me ASAP)

Question

A ship travels at 30 knots from its home port on a course of 97 degree for 2 hours and then changes to a course of 187 degree for 2 hours. Find the distance and bearing of the home port to the ship.

Answer 1

1) Draw the coordinate x & y axes

2) Decompose the displacement vectors into their x & y components

(be careful with the signs)

3) Add the corresponding x and y vector components up

4) Use the pythagorean theorem to find the resultant magnitude from the x component and y component of the resulttant.

5) Use the inverse tangent function (arctangent function) with the y component over the x component to get

an angle in degrees

(IMPORTANT NOTE, inverse tangent function (arctangent function) only outputs either quadrant I or IV. We know the angle should be in quadrant II, essentially a reference angle to the -x axis. Thus, after finding alpha_resultant, subtract from 180 degrees to get the final bearing heading.

Answer 2

This is easier than it seems at first reading. No trig is needed

Draw a figure. The answer should be obvious from looking at the figure,

The ship's course is an isosceles right triangle.

The hypotenuse is √2 times the leg and the bearing is 142°