New
New
Year 10
Foundation

Problem solving with bearings

I can use my knowledge of bearings to solve problems.

New
New
Year 10
Foundation

Problem solving with bearings

I can use my knowledge of bearings to solve problems.

Lesson details

Key learning points

  1. Right-angled trigonometry may be useful when dealing with bearings.
  2. Right-angled trigonometry can help you calculate more information.
  3. Angle facts can be a simpler way of deducing information.

Common misconception

Pupils do not measure the angle from North and simply measure the angle between two line segments.

Reiterate bearings are always measured from North, in a clockwise direction and stated as 3 figures. Encourage pupils to draw North on the correct position before attempting the question.

Keywords

  • Transversal - A transversal is a line, line segment, or ray that intersects through two or more lines at distinct (different) points.

  • Corresponding - Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

  • Alternate - Alternate angles are a pair of angles, both between or both outside two line segments, that are on opposite sides of the transversal that cuts them.

  • Co-interior - Co-interior angles are on the same side of the transversal line and in between the two other lines.

  • Bearing - A bearing is an angle measured in degrees from North in the clockwise direction and written with three figures.

When the bearing from A to B is acute or reflex, some pupils may find a short cut to the solution without understanding why this works. The use of algebra to represent a bearing shows how these short cuts work. When using algebra, check with numerical angles.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Loading...

6 Questions

Q1.
Knowing all North indicators are (North is the same direction) allows us to use a range of angle facts to work out bearings.
Correct answer: parallel
equal in length
wonky
perpendicular to one another
Q2.
The bearing from a plane to the ship is 083°. Work out the bearing from the ship to the plane.
097°
113°
166°
Correct answer: 263°
Q3.
The bearing from Oak City to Acorn Town is 138°. Work out the bearing from Acorn Town to Oak City.
042°
42°
142°
Correct answer: 318°
Q4.
Match the interior angle for each of the following regular polygons.
Correct Answer:Equilateral triangle,60°

60°

Correct Answer:Square,90°

90°

Correct Answer:Pentagon,108°

108°

Correct Answer:Hexagon,120°

120°

Q5.
Which of these is a correct formula for using the tangent function?
Correct answer: $$\tan(x) = \frac{\text{opp}}{\text{adj}}$$
$$\tan(x) = \frac{\text{adj}}{\text{opp}}$$
$$\tan(x) = \frac{\text{opp}}{\text{hyp}}$$
$$\tan(x) = \frac{\text{hyp}}{\text{adj}}$$
Q6.
Given a right-angled triangle, the opposite length is 2 cm and the adjacent length is 3 cm, work out the angle formed between the adjacent and the hypotenuse. Give your answer to 1 d.p.
Correct Answer: 33.7, 33.7°, 33.7 degrees

6 Questions

Q1.
Match the bearing with the statements.
Correct Answer:Due South,has a bearing of 180°

has a bearing of 180°

Correct Answer:Due West,has a bearing of 270°

has a bearing of 270°

Correct Answer:Due East,has a bearing of 090°

has a bearing of 090°

Correct Answer:Due North-East,has a bearing of 045°

has a bearing of 045°

Correct Answer:Due South-East,has a bearing of 135°

has a bearing of 135°

Correct Answer:Due South-West,has a bearing of 225°

has a bearing of 225°

Q2.
Three towns form an equilateral triangle; X, Y and Z. Z is due East from X.
An image in a quiz
Correct Answer:Bearing from X to Y,030°

030°

Correct Answer:Bearing from Y to X,210°

210°

Correct Answer:Bearing from X to Z,090°

090°

Correct Answer:Bearing from Z to X,270°

270°

Q3.
B is 7 km due East from A. C is 4 km due North from B. D is 3 km due West from C. Using squares, where the length of 1 square is 1 km work out the bearing from A to D.
Correct answer: 045°
090°
135°
270°
Q4.
Using the diagram, work out the bearing from C to A.
An image in a quiz
140°
190°
240°
Correct answer: 250°
260°
Q5.
Identify which of the following are always true, sometimes true or never true.
Correct Answer:Always true,The sum of co-interior angles is always 180°

The sum of co-interior angles is always 180°

Correct Answer:Never true,Angles around a point sum to 180°

Angles around a point sum to 180°

Correct Answer:Sometimes true,If the bearing from A to B is $$x$$° then B to A is 180°+ $$x$$°

If the bearing from A to B is $$x$$° then B to A is 180°+ $$x$$°

Q6.
A boat travels due South from port A for 5 km. It then travels due West and arrives at port B . The straight line distance from A to B is 15 km. What is the bearing from B to A?
Correct Answer: 071°, 071