Stage 8 - Q1 - 2 marks
Find the reverse of bearing \(035^{\circ}\).
Hint
Add a half turn.
Stage 8 - Q2 - 2 marks
Find the reverse of bearing \(287^{\circ}\).
Hint
Subtract a half turn because the bearing exceeds 180 degrees.
Stage 8 - Q3 - 2 marks
A boat returns from B to A on bearing \(012^{\circ}\). What was the bearing of its straight outward route A to B?
Hint
The outward and return routes are opposite rays.
Stage 8 - Q4 - 2 marks
From O, A has bearing \(045^{\circ}\) and B has bearing \(140^{\circ}\). Find the smaller angle AOB.
Hint
Both bearings start at the same point.
Stage 8 - Q5 - 3 marks
From O, A has bearing \(350^{\circ}\) and B has bearing \(025^{\circ}\). Find the smaller angle AOB.
Hint
Do not automatically use the larger numerical difference.
Stage 8 - Q6 - 3 marks
A to B has bearing \(065^{\circ}\) and B to C has bearing \(310^{\circ}\). Find the smaller angle ABC.
Hint
Reverse AB before finding an angle at B.
Stage 8 - Q7 - 4 marks
A to B has bearing \(120^{\circ}\) and B to C has bearing \(220^{\circ}\). Explain why \(220-120\) does not give angle ABC, then find that angle.
Hint
An interior angle uses two rays from its own vertex.
Stage 8 - Q8 - 5 marks
AB and BC have equal length. A to B has bearing \(070^{\circ}\), while B to C has bearing \(160^{\circ}\). Find angle ABC and then bearing A to C.
Hint
After finding the angle at B, use the isosceles triangle.
Stage 8 - Q9 - 5 marks
From A, B has bearing \(020^{\circ}\) and C has bearing \(080^{\circ}\). From B, C has bearing \(140^{\circ}\). Find all three triangle angles.
Hint
Convert all directions at a vertex to bearings from that vertex.
Stage 8 - Q10 - 6 marks
From A, B is on bearing \(040^{\circ}\) and C on \(100^{\circ}\). From B, C is on \(130^{\circ}\). Find all three triangle angles and the bearing of A from C. Verify your angle at C using reverse bearings.
Hint
Use both reverse bearings at C as an independent check.