Worked Example 2: Bearings with Distance and Trigonometry
Part of Bearings — GCSE Mathematics
This study notes covers Worked Example 2: Bearings with Distance and Trigonometry within Bearings for GCSE Mathematics. Revise Bearings in Geometry & Measures for GCSE Mathematics with 19 exam-style questions and 5 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 8
Practice
19 questions
Recall
5 flashcards
Worked Example 2: Bearings with Distance and Trigonometry
A ship sails from port P on a bearing of 120° for 50km. How far east and how far south has it traveled?
Step 1 Draw a diagram
Draw North, then the 120° bearing (measured clockwise from North)
120° is in the SE quadrant (between East at 090° and South at 180°)
Step 2 Find the angle from South
Angle from South = 180° - 120° = 60°
The ship is 60° from South toward East
Step 3 Use trigonometry
Distance East = 50 × sin(60°) = 50 × 0.866 = 43.3 km
Distance South = 50 × cos(60°) = 50 × 0.5 = 25 km