Question 1: A boat leaves port heading on a bearing of 045°. It then changes course to a bearing of 135°. Calculate the angle between the two bearings.

Answer: 45

Question 2: A plane is flying on a bearing of 210°. It then adjusts its heading to a bearing of 330°. What is the size of the turn in degrees?

Answer: 120

Question 3: Construct a triangle on the grid with sides of 5 cm, 7 cm, and 9 cm, and label all angles. Calculate the bearing from one vertex to another using the constructed diagram.

Answer: Dependent on diagram; students to use trigonometry and bearing calculation.

Question 4: A ship heads on a bearing of 060°. After sailing 10 km, it changes course to a bearing of 150°. Calculate the distance the ship travels after changing course if it ends up 8 km from its starting point.

Answer: Use cosine rule to find distance; answer approximately 12.65 km.

Question 5: A hiker starts at point A and walks on a bearing of 030° for 4 km to point B. From B, they walk on a bearing of 120° for 3 km to point C. What is the bearing from C back to A?

Answer: Approximate bearing: 300°

Question 6: A car travels on a bearing of 090° for 15 km, then turns to a bearing of 270° and continues for 10 km. What is the total change in bearing?

Answer: 180

Question 7: A lighthouse is situated at the top of a cliff. From a boat 5 km away, the bearing to the lighthouse is 045°. After sailing 3 km further, the bearing changes to 060°. Calculate how far the boat is from the lighthouse now.

Answer: Approximate distance: 4.55 km

Question 8: A drone flies on a bearing of 315° for 6 km, then adjusts to a bearing of 135°. How far does the drone travel after the adjustment if it ends up 8 km from its starting point?

Answer: Approximate distance: 10 km

Question 9: Identify and correct the mistake in the following reasoning: 'If a bearing changes from 045° to 225°, then the turn is 180°.'

Answer: Correct reasoning; the change is 180°, no mistake.

Question 10: A cyclist starts riding on a bearing of 100° for 7 km. They then turn to a bearing of 280° and ride for 5 km. Calculate the total change in bearing and explain your reasoning.

Answer: Change in bearing: 180°, explanation involves subtracting angles considering direction change.

Question 11: A ship needs to head from port to an island 20 km away on a bearing of 045°, then change course to 135° to reach the second part of the journey. If the ship's course change is incorrect, what is a common mistake students make in calculating such bearings?

Answer: Confusing the difference in bearings with the actual angle between directions; misunderstanding angle calculations.