1. ## Trigonometry: Bearings

An oil tanker sails from a port P to port Q, 20km away and on a bearing of 110 degrees from P. After reaching Q, it sets sail to R, 15 km away and on a bearing of 150 degrees from Q. It then proceeds to sail to S, a port 20 km away and on a bearing of 050 degrees from R. Draw a sketch to indicate the relative positions of the ports P, Q, R and S. Calculate
a) how far south of P is S
b) how far east of P is S
c) the bearing of S from P.

2. Did you make your sketch?

Using trigonometric ratios, you'll see that for the part A, S is $20\cos20 + 15\cos60 - 20\cos50$

What about you posting what you tried so far?

3. Originally Posted by Ilsa
An oil tanker sails from a port P to port Q, 20km away and on a bearing of 110 degrees from P. After reaching Q, it sets sail to R, 15 km away and on a bearing of 150 degrees from Q. It then proceeds to sail to S, a port 20 km away and on a bearing of 050 degrees from R. Draw a sketch to indicate the relative positions of the ports P, Q, R and S. Calculate
a) how far south of P is S
b) how far east of P is S
c) the bearing of S from P.
Note the attached diagram with displacement vectors and their respective components ...

x - components

y - components

determine the angles relative to East and use your knowledge of right triangle trig to answer the questions.