Answer the following:

Question

A ship leaves a port and sails for 4 hours on a course of 78° at 18 knots. Then the ship changes its course to 168° and sails for 6 hours at 16 knots. After the 10 hours (a) what is the distance of the ship from the port and (b) what is the bearing from the port to the ship?

Answer 1

You can solve this problem in an easier way than you might have guessed. Note that the angles are 90° apart.

Thus, we can use the Pythagorean Theorem for distance traveled and arctan + 78° to get the orientation.

4*18 = 72

6*16 = 96

Then, note that we have multiple of a 3-4-5 right triangle, as 72 = 3 * 24 and 96 = 4 * 24.

5 * 24 = 120 knots

The bearing is 78º + arctan 4/3 = 131.13° or 131°8'