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

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

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

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

Problem solving with bearings

Maths

In the angles unit, pupils reasoned through more complex problems involving angles. In the bearings unit, pupils apply their knowledge of angles in order to calculate bearings and solve angle problems within the context of bearings.

Bearings

Three towns form an equilateral triangle; X, Y and Z. Z is due East from X.

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.

Using the diagram, work out the bearing from C to A.

The sum of co-interior angles is always 180°

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

Identify which of the following are always true, sometimes true or never true. 

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?

Knowing all North indicators are {{}} (North is the same direction) allows us to use a range of angle facts to work out bearings.

The bearing from a plane to the ship is 083°. Work out the bearing from the ship to the plane.

The bearing from Oak City to Acorn Town is 138°. Work out the bearing from Acorn Town to Oak City.

Match the interior angle for each of the following regular polygons. 

$$\tan(x) = \frac{\text{opp}}{\text{adj}}$$

$$\tan(x) = \frac{\text{adj}}{\text{opp}}$$

$$\tan(x) = \frac{\text{opp}}{\text{hyp}}$$

$$\tan(x) = \frac{\text{hyp}}{\text{adj}}$$

Which of these is a correct formula for using the tangent function?

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.

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