Bearings Constructions And Scale Drawings

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Bearings

Bearings are a way of describing an angle, commonly used in navigation.
Three rules: measured from North, measured clockwise, written with 3 digits (e.g., 059°).
Compass directions have standard bearings: N=000°, E=090°, S=180°, W=270°.
To find bearing of B from A: start at A, draw North line, measure clockwise angle to B.
If bearing of A from B is <180°, add 180° to get bearing of B from A; if >180°, subtract 180°.
Always draw a clear diagram and label angles carefully.

Bearings of compass points

Scale

Scale is a ratio comparing drawn size to real-life size (e.g., 1:50000).
To find actual distance: measure on drawing, multiply by scale factor, convert units.
To find drawing length: convert actual distance to same units, divide by scale factor.
Common conversions: 1 km = 1000 m = 100000 cm.
Always check if answer is sensible (e.g., actual distance > drawing distance).

Constructing Triangles (SSS)

SSS triangle construction uses three given side lengths.
Tools: pencil, ruler, compasses.
Step 1: Draw the longest side as base using ruler.
Step 2: Set compass to one side length, draw arc from one endpoint above base.
Step 3: Set compass to third side length, draw arc from other endpoint to intersect first arc.
Step 4: Draw lines from base endpoints to intersection point.
Do not erase construction arcs – they show your method.
Label vertices and side lengths as required.

Constructing triangle ABC

Scale Drawings

Scale drawing uses a given scale to represent real objects or distances.
Use ruler and protractor for accurate measurements and bearings.
To mark a point given distance and bearing: draw North line, measure bearing clockwise, draw line to scale distance.
For combined conditions (e.g., within distance range and bearing range), construct and shade the region.
Always leave construction lines and arcs visible for marks.

Plotting a route by bearing and scale

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1.What are the three rules for bearings?
Easy
- AMeasured from North, clockwise, written with three digits
- BMeasured from South, anticlockwise, written with three digits
- CMeasured from East, clockwise, written with two digits
- DMeasured from North, anticlockwise, written with three digits
2.The bearing of B from A is 105°. What is the bearing of A from B?
Medium
- A285°
- B075°
- C255°
- D195°
3.A map has a scale of 1:50000. What does 1 cm on the map represent in real life?
Easy
- A50000 cm
- B5000 cm
- C500 m
- D5 km
4.In a scale drawing, 1 cm represents 40 cm. If the window on the drawing is 3 cm long and 2 cm high, what are the actual dimensions?
Easy
- A120 cm by 80 cm
- B40 cm by 30 cm
- C12 cm by 8 cm
- D160 cm by 120 cm
5.Using a ruler and compasses only, to construct a triangle with sides 5 cm, 7 cm and 9 cm, which side should you draw first?
Medium
- AThe longest side (9 cm)
- BThe shortest side (5 cm)
- CAny side, it doesn't matter
- DThe side of length 7 cm
6.What is the compass direction for a bearing of 090°?
Easy
- AEast
- BNorth
- CWest
- DSouth
7.The bearing of a lighthouse from a boat is 135°. What is the bearing of the boat from the lighthouse?
Medium
- A315°
- B045°
- C225°
- D135°
8.On a map with scale 1:150000, the distance between two towns is 5.8 cm. What is the actual distance in km?
Medium
- A8.7 km
- B87 km
- C0.87 km
- D870 km

Mehr Fragen

9.In triangle ABC, AB = 6 cm, BC = 7 cm, AC = 8 cm. Using a ruler and compasses, which step comes after drawing the base AB?
Medium
- ADraw an arc from A with radius 8 cm and from B with radius 7 cm
- BDraw an arc from A with radius 7 cm and from B with radius 8 cm
- CDraw a line from A to C
- DMeasure angle ABC
10.The bearing of town T from town S is 073°. What is the bearing of S from T?
Medium
- A253°
- B107°
- C287°
- D073°
11.A scale drawing uses 1 cm to represent 15 km. On the drawing, the distance between two towns is 4.2 cm. What is the actual distance?
Easy
- A63 km
- B42 km
- C15 km
- D6.3 km
12.The bearing of D from E is 245°. Find the bearing of E from D.
Medium
- A065°
- B115°
- C295°
- D205°
13.On a map of scale 1:50000, a park measures 3.4 cm by 2.1 cm. What is the actual area of the park in square kilometres?
Hard
- A1.785 km²
- B178.5 km²
- C0.1785 km²
- D17.85 km²
14.In a construction of an equilateral triangle with side length 5 cm, what is the radius of the arcs drawn from each endpoint of the base?
Easy
- A5 cm
- B10 cm
- C2.5 cm
15.The scale of a map is 1:25000. The distance between two points on the map is 8.4 cm. What is the actual distance in metres?
Medium
- A2100 m
- B210 m
- C21000 m
- D2.1 m
16.The bearing of a ship from a lighthouse is 240°. What is the bearing of the lighthouse from the ship?
Medium
- A060°
- B120°
- C240°
17.On a scale drawing, 1 cm represents 5 m. What is the actual length of a wall that is 8.2 cm on the drawing?
Easy
- A41 m
- B1.64 m
- C82 m
- D4.1 m
18.The bearing of B from A is 127°. What is the bearing of A from B?
Medium
- A307°
- B053°
- C127°
- D233°
19.A map has a scale of 1:25000. How many metres does 1 cm on the map represent?
Easy
- A250 m
- B25 m
- C2500 m
- D2.5 m
20.In a triangle construction, you are given side lengths 4 cm, 5 cm, and 6 cm. Which side should you draw first?
Easy
- A6 cm
- B4 cm
- C5 cm
- DAny side
21.The scale drawing shows two towns A and B. The scale is 1 cm to 12 km. The distance on the map is 4.5 cm. What is the actual distance?
Easy
- A54 km
- B48 km
- C60 km
- D36 km
22.A bearing of 045° corresponds to which compass direction?
Easy
- ANorth-East
- BNorth
- CEast
- DNorth-West
23.When constructing a triangle with sides 5 cm, 6 cm, and 7 cm, what is the first step after drawing the base?
Easy
- ASet compass to 6 cm and draw an arc from one end
- BSet compass to 7 cm and draw an arc from one end
- CDraw the third side
- DMeasure the angles
24.The bearing of a lighthouse from a boat is 315°. What is the bearing of the boat from the lighthouse?
Medium
- A135°
- B045°
- C315°
- D225°
25.On a map with scale 1:200000, a lake has an area of 2.5 cm². What is the actual area in km²?
Medium
- A10 km²
- B1 km²
- C100 km²
- D0.1 km²
26.In triangle ABC, AB = 8 cm, BC = 6 cm, AC = 7 cm. Using a ruler and compasses, which arc radii are used?
Easy
- A6 cm and 7 cm
- B8 cm and 6 cm
- C8 cm and 7 cm
- D6 cm and 8 cm
27.What is the compass direction for a bearing of 270°?
Easy
- AWest
- BEast
- CNorth
- DSouth
28.A map scale is 1:100000. How many cm on the map represent an actual distance of 8 km?
Medium
- A8 cm
- B0.8 cm
- C80 cm
- D0.08 cm
29.The bearing of P from Q is 250°. Find the bearing of Q from P.
Medium
- A070°
- B110°
- C250°
- D190°
30.A ship sails from port A on a bearing of 060° for 120 km to point B. It then sails from B on a bearing of 150° for 80 km to point C. What is the bearing of C from A? (You may assume a scale drawing is not required; use trigonometry if needed.)
Hard
- A094°
- B060°
- C090°
- D124°
31.A map has a scale of 1:50000. The area of a forest on the map is 8 cm². What is the actual area of the forest in square kilometres?
Medium
- A2 km²
- B20 km²
- C0.2 km²
- D200 km²
32.In triangle ABC, AB = 8 cm, BC = 6 cm, AC = 7 cm. Using a ruler and compasses only to construct triangle ABC, what is the correct order of steps after drawing side AB?
Medium
- ADraw an arc from A with radius 7 cm, then an arc from B with radius 6 cm, and join intersection to A and B.
- BDraw an arc from A with radius 6 cm, then an arc from B with radius 7 cm, and join intersection to A and B.
- CDraw arcs from A and B with radius 8 cm, then join intersection to A and B.
- DDraw a perpendicular bisector of AB, then mark point C at 6 cm from B.
33.A circular garden has a diameter of 11.4 m. Using a scale of 1 cm to 1.5 m, what is the radius of the circle drawn on the plan?
Medium
- A3.8 cm
- B7.6 cm
- C5.7 cm
- D2.85 cm
34.In triangle ABC, AB = 8.5 cm, BC = 7.6 cm and AC = 6.2 cm. Using a ruler and compasses only to construct triangle ABC, which side must be drawn first?
Easy
- AAB
- BBC
- CAC
- DAny side can be drawn first
35.A map scale is 1:25000. A rectangular park measures 3.4 cm by 2.1 cm on the map. What is the actual area of the park in square metres?
Hard
- A446250 m²
- B446.25 m²
- C4462500 m²
- D44.625 m²
36.The bearing of P from Q is 073°. What is the bearing of Q from P?
Medium
- A253°
- B107°
- C073°
- D287°
37.Which compass direction corresponds to a bearing of 180°?
Easy
- ANorth
- BEast
- CSouth
- DWest
38.Bearings are always measured clockwise from North.
Easy
True or false?
39.A bearing of 045° is equivalent to which compass direction?
Easy
- ANorth
- BNorth-East
- CEast
- DNorth-West
40.To construct a triangle with sides 5 cm, 6 cm, and 7 cm, which side should you draw first?
Easy
- A5 cm
- B6 cm
- C7 cm
- DAny side is fine
41.In a scale drawing, 1 cm represents 40 cm. If a window on the drawing is 3 cm long and 2 cm high, what are the actual dimensions?
Medium
- A120 cm by 80 cm
- B12 cm by 8 cm
- C7 cm by 6 cm
- D40 cm by 30 cm
42.Match each compass direction to its bearing.
Easy
- North
- East
- South
- West
- 000°
- 090°
- 180°
- 270°
43.Arrange the following steps in the correct order to construct a triangle with sides 6 cm, 7 cm, and 10 cm using a ruler and compasses.
Medium
- Draw the 10 cm side as the base.
- Set compasses to 6 cm and draw an arc from one end of the base.
- Set compasses to 7 cm and draw an arc from the other end of the base.
- Draw lines from each end of the base to the intersection of the arcs.
44.The bearing of a point B from A is always measured clockwise from North at point A.
Easy
True or false?
45.Which of the following are correct rules for bearings? (Select all that apply)
Medium
- ABearings are measured clockwise from North.
- BBearings are always written with three digits.
- CBearings can be measured anticlockwise from South.
- DThe bearing of A from B is the same as the bearing of B from A.
- EA bearing of 045° means the direction is Northeast.
46.A ship sails from port P on a bearing of 040° for 120 km to point Q. It then sails from Q on a bearing of 130° for 90 km to point R. What is the bearing of R from P, to the nearest degree?
Hard
- A077°
- B040°
- C130°
- D053°
47.On a map with scale 1:100000, how many kilometres does 1 cm represent?
Easy
48.A map has a scale of 1:50000. The distance between two towns on the map is 3.6 cm. What is the actual distance in kilometres?
Medium
49.Fill in the blanks to complete the three rules for bearings.
Easy
Bearings are measured from ____. They are measured ____. The angle should always be written with ____ digits.
50.A map scale is 1:200000. How many centimetres on the map represent an actual distance of 5 km?
Medium
51.What is the bearing of East? (Write your answer as a three-digit number.)
Easy
52.A map has a scale of 1 : 200 000. The distance between two towns on the map is 4.5 cm. What is the actual distance in kilometres?
Medium
53.Fill in the blanks with the correct numbers.
Easy
A bearing is measured clockwise from ____. It is always written with ____ digits.
54.Explain how to find the bearing of B from A if the bearing of A from B is 250°.
Hard
55.On a map with scale 1:100000, how many kilometres does 1 cm represent?
Easy
- A1 km
- B2 km
- C3 km
- D0 km
56.A map has a scale of 1:50000. The distance between two towns on the map is 3.6 cm. What is the actual distance in kilometres?
Medium
- A2.8 km
- B1.8 km
- C0.8 km
- D3.8 km
57.A map scale is 1:200000. How many centimetres on the map represent an actual distance of 5 km?
Medium
- A4.5 cm
- B2.5 cm
- C3.5 cm
- D1.5 cm
58.A map has a scale of 1 : 200 000. The distance between two towns on the map is 4.5 cm. What is the actual distance in kilometres?
Medium
- A9 km
- B11 km
- C10 km
- D8 km

Lernnotizen

## Bearings, Constructions & Scale Drawings ### Bearings - **Definition**: A bearing is an angle measured clockwise from North, written as three digits (e.g., 059°). - **Rules**: 1. Measured from North. 2. Measured clockwise. 3. Always written with 3 figures. - **Finding a bearing**: Start at the point after "from". Draw a North line, measure clockwise to the line joining the points. - **Reverse bearing**: If bearing of A from B is less than 180°, add 180°; if more than 180°, subtract 180°. ### Scale - **Definition**: A ratio comparing drawn size to real size. E.g., 1:50000 means 1 cm on map = 50000 cm in real life. - **Using scale to find actual length**: Measure on map, multiply by scale factor, convert units. - **Using scale to find drawn length**: Convert actual distance to same units, divide by scale factor. ### Constructing Triangles (SSS) - **Equipment**: Pencil, ruler, compasses. - **Steps**: 1. Draw the longest side as base. 2. Set compass to one side length, draw arc from one endpoint. 3. Set compass to third side, draw arc from other endpoint to intersect. 4. Connect endpoints to intersection. 5. **Do not erase construction arcs** (they earn marks). ### Tips - Always draw a clear diagram. - Use a sharp pencil and accurate ruler/protractor. - For bearings, label North lines.

Bearing: An angle measured clockwise from North, written with three digits (e.g., 059°).
Scale: A ratio that describes the relationship between the drawn size and the real-life size (e.g., 1:50000).
SSS Triangle Construction: Drawing a triangle accurately given the lengths of its three sides using a ruler and compasses.
Construction Arcs: Arcs drawn with compasses during construction; must not be erased as they show method.

Karteikarten

What are the three rules for bearings?

Measured from North, measured clockwise, and written with three digits (e.g., 059°).

How do you find the bearing of B from A?

Start at A, draw a North line, measure the clockwise angle from North to the line AB, and write it as three digits.

If the bearing of A from B is 105°, what is the bearing of B from A?

Add 180°: 105° + 180° = 285°.

If the bearing of A from B is 245°, what is the bearing of B from A?

Subtract 180°: 245° - 180° = 065°.

What is the bearing of East?

090°.

What is the bearing of South?

180°.

What is the bearing of West?

270°.

What is the bearing of North?

000° or 360°.

A map scale is 1 cm represents 10 km. What is the scale as a ratio?

1 : 1 000 000 (since 10 km = 1 000 000 cm).

On a map with scale 1:50 000, a distance measures 5.8 cm. What is the actual distance in km?

5.8 cm × 50 000 = 290 000 cm = 2.9 km.

How do you construct an SSS triangle with sides 6 cm, 7 cm, and 10 cm?

Draw the 10 cm base. Using compasses, draw an arc of radius 6 cm from one end and an arc of radius 7 cm from the other end. The intersection is the third vertex. Connect and label sides.

Why should you not erase construction arcs in triangle constructions?

Examiners use the arcs to verify that the triangle was constructed accurately.

How do you construct an equilateral triangle with side AB given?

Set compasses to length AB. Draw arcs from A and B above AB. The intersection is C. Connect A to C and B to C.

A scale drawing uses 1 cm to represent 40 cm. The window on the drawing is 3 cm long and 2 cm high. Find actual length and height.

Length = 3 × 40 = 120 cm; Height = 2 × 40 = 80 cm.

On a map, 1 cm represents 15 km. The distance between two towns on the map is 4.5 cm. Find actual distance.

4.5 × 15 = 67.5 km.

How do you mark a point C on a scale drawing given its distance and bearing from A?

Draw a North line at A. Measure the bearing clockwise from North. Draw a line in that direction. Measure the scaled distance along that line to mark C.

The bearing of B from A is 073°. Find the bearing of A from B.

073° + 180° = 253°.

What equipment is needed for SSS triangle construction?

Pencil, ruler, and a pair of compasses.

A map scale is 1:500 000. Convert this to 1 cm represents how many km?

1 cm represents 5 km (since 500 000 cm = 5 km).

How do you find the actual distance from a scale drawing if the scale is given as a ratio?

Measure the distance on the drawing in cm, multiply by the scale factor, then convert to suitable units.

In triangle ABC, BC = 7.6 cm and AC = 6.2 cm. AB is drawn. How do you construct the triangle?

Set compasses to 6.2 cm, draw an arc from A. Set to 7.6 cm, draw an arc from B. Intersection is C. Connect A-C and B-C.

A field ABC has AC = 500 m and BC = 650 m. Scale 1 cm = 100 m. AB is drawn. How to complete the scale drawing?

Convert: AC = 5 cm, BC = 6.5 cm. Draw arcs of these radii from A and B to find C.

What is the bearing of a point directly west of another?

270°.

A circular garden has diameter 11.4 m. Scale 1 cm = 1.5 m. What is the diameter on the drawing?

11.4 ÷ 1.5 = 7.6 cm.

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