Bearings and Scale Word Problems Worksheet | Cazoom Maths Worksheets - Free Printable

Let's solve each problem step by step.

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Problem 1:

An airplane is at a bearing of \(040^\circ\) from Manchester and \(285^\circ\) from Sheffield. Show its position on the map below.

#### Solution:
1. Understand Bearings:
- A bearing is measured clockwise from the north direction.
- From Manchester, the airplane is at \(040^\circ\).
- From Sheffield, the airplane is at \(285^\circ\).

2. Draw the Bearings:
- Draw a line from Manchester at \(040^\circ\) (measured clockwise from North).
- Draw a line from Sheffield at \(285^\circ\) (measured clockwise from North).

3. Find the Intersection:
- The point where these two lines intersect is the position of the airplane.

#### Final Answer:
- Mark the intersection of the two lines as the position of the airplane.

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Problem 2:

Ship A is due east of Ship B. Ship A and Ship B travel back to the Port, P. The bearing of P from A is \(052^\circ\). The bearing of P from B is \(300^\circ\). Mark the position of P on the scale drawing below.

#### Solution:
1. Understand the Setup:
- Ship A is due east of Ship B, so the line connecting them is horizontal.
- The bearing of P from A is \(052^\circ\).
- The bearing of P from B is \(300^\circ\).

2. Draw the Bearings:
- From Ship A, draw a line at \(052^\circ\) (measured clockwise from North).
- From Ship B, draw a line at \(300^\circ\) (measured clockwise from North).

3. Find the Intersection:
- The point where these two lines intersect is the position of Port P.

#### Final Answer:
- Mark the intersection of the two lines as the position of Port P.

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Problem 3:

The diagram shows Tim’s house H and the school S.
- Scale: \(1 \, \text{cm} = 120 \, \text{m}\)

#### Part (a): Use the diagram to work out the actual distance from Tim’s house to the school.
1. Measure the Distance on the Diagram:
- Measure the distance between points H and S on the diagram using a ruler.
- Let's say the measured distance is \(d \, \text{cm}\).

2. Convert to Actual Distance:
- The scale is \(1 \, \text{cm} = 120 \, \text{m}\).
- Actual distance = \(d \times 120 \, \text{m}\).

#### Part (b): Measure and write down the three-figure bearing of the school from Tim’s house.
1. Measure the Bearing:
- Place a protractor at point H with the north direction aligned.
- Measure the angle from the north direction to the line connecting H to S.
- Ensure the bearing is a three-figure bearing (e.g., \(035^\circ\)).

#### Part (c): The park P is \(360 \, \text{m}\) from the school on a bearing of \(110^\circ\). Mark the position of P on the diagram.
1. Convert the Distance to Scale:
- The scale is \(1 \, \text{cm} = 120 \, \text{m}\).
- Distance on the diagram = \(\frac{360}{120} = 3 \, \text{cm}\).

2. Draw the Bearing:
- From point S, draw a line at \(110^\circ\) (measured clockwise from North).
- Measure \(3 \, \text{cm}\) along this line and mark the point as P.

#### Final Answers:
- Part (a): Actual distance = \(d \times 120 \, \text{m}\) (where \(d\) is the measured distance in cm).
- Part (b): Three-figure bearing of S from H (measure using a protractor).
- Part (c): Mark the point P on the diagram as described.

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Final Boxed Answers:

1. Airplane Position: Mark the intersection of the \(040^\circ\) line from Manchester and the \(285^\circ\) line from Sheffield.
2. Port P Position: Mark the intersection of the \(052^\circ\) line from Ship A and the \(300^\circ\) line from Ship B.
3. Part (a): Actual distance = \(d \times 120 \, \text{m}\).
4. Part (b): Three-figure bearing of S from H (measure using a protractor).
5. Part (c): Mark the point P on the diagram as described.

\[
\boxed{\text{See detailed steps above for final markings and calculations.}}
\]