1. 17 Trigonometry Compass Directions N S N S N 45° E 45° E W E W 30°
E 30° S N S N S
W 60° N
60° E W E W
20°
S 20° W

2. 17 Trigonometry Compass Directions N B W E 6 km 4 km N S C W E A S
A ship leaves a port A and sails a distance of 4 km in the direction N 30° E to a point B. The ship then changes direction and sails for a further 6 km in the direction S 60° E to a point C.
(i) Calculate the distance from the ship’s present position at point C to port A.
(ii) Find |∠BCA|, to the nearest degree.
(iii) Hence, find the direction of C from A. N S E W
30° B
60°
6 km
4 km N S E W
30° C A

3. 17 Trigonometry Compass Directions B 6 km 4 km C A
(i) Calculate the distance from the ship’s present position at point C to port A.
4 km
6 km
90° C A B
|AC|2 = (Theorem of Pythagoras)
|AC|2 = 16+36
|AC|2 = 52
|AC| = 52
∴ |AC| = 7.2 km, to 1 decimal place

4. 17 Trigonometry Compass Directions B Adjacent Opposite 4 km 6 km C A
(ii) Find |∠BCA|, to the nearest degree.
4 km
6 km
90° C A B
Opposite
Adjacent 𝜽°
tan 𝜃= 4 6
𝜃=ta n −
𝜃= …°  
∴ |∠BCA| = 34°, to nearest degree

5. 17 Trigonometry Compass Directions B 6 km N 4 km N W E C W E A 4° S S
(iii) Find the direction of C from A. N S E W
30°
60° A C
4 km
6 km B
30° N S W E
34°
30°
34°− 30° =4° 4°
Hence, the direction of C from A is E 4° N.