Applications in Bearings and Navigation
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Applications in Bearings and Navigation — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionMulti-Step Navigation ProblemsConcept Practice
2 marks~3 minCriterion A
A coast guard vessel is at point PP and a lighthouse is at point QQ. The diagram shows a north arrow at PP and the line PQPQ.

The angle measured clockwise from north to line PQPQ is 47°47°.
a
Deduce the three-figure bearing of QQ from PP. [1]
b
The coast guard must sail on a bearing between 040°040° and 055°055° to stay within a safe navigation corridor. Justify whether the vessel is heading within the safe corridor. [1]
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Solutions

2QuestionSolving Bearings Questions Using TrigonometryAssessment Practice
6 marks~9 minCriterion D
A search-and-rescue helicopter uses bearings from two coastal stations, A and B, which are 12 km apart along a straight coastline. Station A reports a distress signal at a bearing of 055°055°, and station B reports it at a bearing of 320°320°. The helicopter crew triangulates the signal position, assuming a flat Earth and that bearings are accurate to within ±1°\pm 1°.
a
Calculate the distance from station A to the distress signal. Show all working. [2]
b
Explain how the bearing uncertainty of ±1°\pm 1° affects the size of the search zone and how the flat-Earth assumption may limit the accuracy of this model. [2]
c
Justify whether bearing-based triangulation provides a sufficiently reliable method for directing the helicopter to the distress signal in this scenario. [2]
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Solutions

3QuestionUnderstanding Bearings as Directional AnglesAssessment Practice
6 marks~9 minCriterion C
A port is located at the origin (0,0)(0, 0) and a lighthouse is at coordinates (3,4)(3, 4) km, where the positive xx-axis points east and the positive yy-axis points north. A student proposes the following model to calculate the bearing of the lighthouse from the port:

θ=tan⁡−1 ⁣(xy),B=90°−θ\theta = \tan^{-1}\!\left(\frac{x}{y}\right), \qquad B = 90° - \theta
a
Calculate the bearing BB predicted by the student's model. [2]
b
Construct the correct bearing using a clearly labelled diagram and trigonometric reasoning. [2]
c
The lighthouse is the destination of a vessel that must follow a bearing accurate to within ±2°\pm 2° to avoid shallow waters. Advise the navigator whether the student's model should be used for this voyage, identifying the source of any error in the model. [2]
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Solutions

4QuestionMulti-Step Navigation ProblemsAssessment Practice
12 marks~18 minCriterion B
A small boat completes two-leg voyages. The captain records the bearing and distance of each leg.

Voyage 1: Leg 1: 045°045°, 1010 km; Leg 2: 135°135°, 1010 km; Final displacement: 14.114.1 km at 090°090°
Voyage 2: Leg 1: 060°060°, 1515 km; Leg 2: 120°120°, 1515 km; Final displacement: 26.026.0 km at 090°090°
Voyage 3: Leg 1: 030°030°, 88 km; Leg 2: 150°150°, 88 km; Final displacement: 8.08.0 km at 090°090°
Voyage 4: Leg 1: 000°000°, 55 km; Leg 2: 180°180°, 55 km; Final displacement: 00 km
a
Calculate the sum of the two bearings for each voyage. Deduce what the four sums have in common. [2]
b
For Voyages 1–3, the two leg distances are equal and the bearing sums equal 180°180°. Analyse the final displacement directions and formulate a general rule predicting the direction of the final displacement whenever two legs of equal distance have bearings summing to 180°180°. [4]
c
A navigator plans Voyage 6: Leg 1: 225°225°, 1212 km; Leg 2: 135°135°, 1212 km. Using vector components, calculate the actual final displacement (magnitude and direction). Advise the navigator whether the rule from part (b) can be used to plan this voyage, justifying your advice with reference to both the bearing sum and the calculated result. [6]

Solutions

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