Bearings are the angle of rotation taken clockwise from the vertical, which
is north.
When the ship goes from A to B for 3 hours at 42 knots, it travels (42)(3) =
126 nautical miles.
When the ship goes from B to C for 5 hours at 42 knots, it travels (42)(5) =
210 nautical miles.
We have two sides of the triangle. We need to find the angle between them,
angle ABC. Let's go back to the drawing and calculate it by finding its
two parts and adding them.
The angle indicated by the green arc is 40° because it and the other 40°
angle at A are alternate interior angles when transversal AB cuts the two
parallel vertical lines at A and B.
The angle indicated by the blue arc is 55° because it is supplementary
to the 125° angle at B.
So we add the two parts 40°+55° = 95°.
We want to find the distance from where the ship started, to where it is
after the 8 hours.
We use the law of cosines:
nautical miles
Now we must get the bearing at C.
The left part of the bearing angle at C is 125° because it and the other
125° angle at B are alternate interior angles when transversal BC cuts the
two parallel vertical lines at B and C. The right part of the bearing
angle at C is simply 180°. When we add them we get 125°+180° = 305°
Distance from A = 254.1422474 nautical miles
Bearing = 305°
Edwin
