What are Bearings?
Bearings in maths determine directions and facilitate effective navigation in the air, on land, or at sea. The Bearing definition describes it as an angle measured clockwise from the North direction to the point. Maths measures bearings from one point to another point and always expresses them in three figures.
For example, I am walking from home to the park at the bearing of 045°.
While preparing for GCSE Maths, you must know how to measure and plot the bearings and find the distance between the two points given the bearings. This article covers all the key steps required to draw and calculate the bearings in a simplified way, including solved examples.
How to draw Bearings?
To draw bearings:
- Find the starting point for your bearing and, if necessary, draw a north line.
- Place the zero on your protractor on the north line and measure the required angle clockwise. Make a mark at the correct angle.
- Draw a line from your starting point in the direction of the bearing. If you're working on a scale drawing and know the distance, use the scale to pinpoint the location accurately.
How to measure bearings?
To measure the bearing from one point to the other:
- Draw a line joining the given two points.
- From the point you need to measure the bearing, draw a North line.
- Now using the protractor, measure the clockwise angle from the North line to the line joining the two points.
- Express the clockwise angle using three figures to get the required bearing.
Example:
The diagram shows two points P and Q on a map. Find the bearing from P to Q.
Solution:
Draw a line joining the given two points.
From the point you need to measure the bearing, draw a North line.
To measure the bearing of Q from P, draw a North line from P.
Now using the protractor, measure the clockwise angle from the North line to the line joining the two points.
Express the clockwise angle using three figures to get the required bearing.
The clockwise angle is 60°, and in three figures is 060°.
Hence, the bearing of Q from P is 060°.
How to solve Bearings?
Bearings are used in navigation to find missing distances (lengths) and directions (angles) and often involve the use of Pythagoras or trigonometry. To solve bearings questions, follow these steps:
- Draw a Diagram: Include all given points and distances.
- Draw a North Line: At the point where you want to measure the bearing, draw a vertical arrow pointing up. For example, if you are given the bearing from A to B, draw the north line at point A.
- Measure the Angle: From the north line, measure the given bearing angle clockwise.
- Draw the Line: Draw a line from the starting point in the direction of the bearing and mark the new point at the given distance.
You may need to use Pythagoras's theorem or trigonometry to calculate any additional distances. Remember, some questions might provide a scale or require you to consider using one. Additionally, understanding angle facts can help find missing directions.
Solved example on bearings and scale drawings
Example:
A man jogs 2 km from point A, at a bearing of 050°. If the scale of the map below is 1 cm to 1 km, how far is the man now from his home?
Solution:
Drawing a line at a bearing of 050° from A.
Use the given scale to mark the point 2 km from A on the line.
Scale is 1 cm = 1 km
So, 2 km = 2 cm
Now measure the distance from the point 3 km from A to the home on the map and use the scale to find the actual distance.
Distance of the man from home = 3.6 cm
Scale is 1 cm = 1 km
Actual distance of the man from his home = 3.6 km
Hence, the man is 3.6 km away from his home.
Top 10 Important questions
Question 1:
Work out the bearing of C from A.
Options :
A) 225°
B) 105°
C) 240°
D) 25°
Answer :C) 240°
Solution :
Question 2:
Here is a map of an island.
A straight road joins the two villages, Sark and Guernsey.
Find the bearing of Guernsey from Sark.
Options :
A) 045°
B) 290°
C) 070°
D) 315°
Answer :C) 070°
Solution :
Question 3:
Points A and B are shown on a centimetre grid.
Determine the direction or bearing of point B for point A..
Options :
A) 045°
B) 090°
C) 180°
D) 270°
Answer :C) 180°
Solution :
Question 4:
Point M is 250 metres west of point N.
Mark point M on the centimetre grid.
Use a scale of 1 centimetre to represent 100 metres.
Options :
A)
B)
C)
D)
Answer : D
Solution :
Question 5:
The diagram shows the position of the towns, Polperro and St Mawes.
The bearing of Polperro from St Mawes is a°.
The bearing of St Mawes from Polperro is 4a°.
Calculate the 3-figure bearing of St Mawes from Polperro.
Options :
A) 45°
B) 52°
C) 72°
D) 60°
Answer :D) 60°
Solution :
Question 6:
A, B and C are three towns.
B is 20 kilometres due East of A.
C is 35 kilometres due South of A.
Work out the bearing of C from B.
Options :
A) 201.2°
B) 250.5°
C) 209.2°
D) 210.8°
Answer : C) 209.2°
Solution :
Question 7:
Becky travels 20 km in a straight line from town A, at a bearing of 060° to reach town B. If the scale of the map below is 1 cm to 5 km, how far is Becky now from the lake?
Options :
A) 24 km
B) 18 km
C) 20 km
D) 16 km
Answer :A) 24 km
Solution :
Question 8:
The bearing of Q from P is 125°. Find the bearing of P from Q.
Options :
A) 310°
B) 305°
C) 290°
D) 275°
Answer : B) 305°
Solution :
Question 9:
R is a radar tower.
A and B are two aircraft.
At 1 am,
- Aircraft A is 4250 km from R on a bearing of 020°.
- Aircraft B is 3950 km from R on a bearing of 070°.
What is the distance between aircrafts A and B at 1 am, upto one decimal place?
Options :
A) 3482.4 km
B) 3476.1 km
C) 1854.4 km
D) 3126.8 km
Answer :B) 3476.1 km
Solution :
Question 10:
A ship sails from A to B, and then from B to C.
B is 10 miles from A, on a bearing of 070°
C is 22 miles from B, on a bearing of 140°
Work out the direct distance from A to C.
Options :
A) 24.2 miles
B) 27.1 miles
C) 18.6 miles
D) 21.7 miles
Answer :B) 27.1 miles
Solution :
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