Trigonometry and Compass Directions Problem Solving
In this trigonometry problem, a ship travels from point A to point B and then to point C in specific directions. By applying the Pythagorean theorem, the distance from point C to A is calculated to be 7.2 km. The angle BCA is determined to be 34 degrees, and the direction of point C from A is found to be E 4 N.
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Trigonometry 17 Compass Directions N N N 45 E 45 E E W W 30 E 30 S S S N N W 60 N 60 E W W E 20 S 20 W S S 1 ACTIVE MATHS 3
Trigonometry 17 Compass Directions 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 B E W 60 6 km 30 4 km N S 30 C E W A S 2 ACTIVE MATHS 3
Trigonometry 17 Compass Directions (i) Calculate the distance from the ship s present position at point C to port A. B 90 6 km 4 km C A |AC|2=42+ 62 (Theorem of Pythagoras) |AC|2=16 + 36 |AC|2=52 |AC| = 52 |AC| =7.2 km, to 1 decimal place 3 ACTIVE MATHS 3
Trigonometry 17 Compass Directions (ii) Find | BCA|, to the nearest degree. B 90 6 km 4 km ? C A tan ? =4 6 ? = tan 14 6 ? = 33.69006 | BCA| = 34 , to nearest degree 4 ACTIVE MATHS 3
Trigonometry 17 Compass Directions (iii) Find the direction of C from A. N B E W 30 60 6 km N 30 4 km N S 34 30 30 W E C E W A 4 S S 34 30 = 4 Hence, the direction of C from A is E 4 N. 5 ACTIVE MATHS 3
