## Angles

This is a reference to the amount of

**turn**between the 2 lines.

That is, if you had a circle and drew a radius from the middle to the top, and then rotated it one quarter of a turn, you would have turned the radius through 90°.

One full turn around a circle is 360°.

This means that every angle formed between the two lines will be something less than that - for example, one quarter is 90°, half is 180°, three quarters is 270°.

### Using a level

**Level** means perfectly horizontal. A spirit level allows you to check that a surface or line is horizontal. It works on the principle that the bubble will find the highest point in a glass tube, because it is lighter than the surrounding fluid.

Since the tube is curved slightly with the highest point in the middle, the bubble floats exactly in the middle when the level is horizontal.

**plumb**.

'Plumb' means perfectly vertical, and comes from a Latin word meaning 'lead'.

This is a reference to the plumb bob, which traditionally was always made of lead.

When a

**plumb bob**is hung from a string, gravity draws the weight downwards, and the string forms a vertical line.

### Measuring diagonals

If you're manufacturing an object that's rectangular in shape, one way of checking the sides for 'square' is to measure the diagonals. This principle works because the opposite sides of a square or rectangle are always **parallel** - that is, the same distance apart at both ends. Therefore, if the corners are square, the two diagonals will be the same length.

It's worth keeping this in mind as a reminder that you can't simply measure the lengths of the sides to check that an item is square - this won't tell you whether the corners are at right angles.

The 3, 4, 5 rule states that if you measure 3 units along one wall and mark the point, and 4 units along the other wall and mark the point, the distance between the two points should be 5 units if the corner is square.

It doesn't matter what length a 'unit' is, as long as the proportions are 3, 4 and 5.

That is, your lengths could be 3 metres, 4 metres, 5 metres; or 3 feet, 4 feet, 5 feet; or 6, 8, 10 or any other multiple of 3, 4, 5.

### Learning activity

Audio 15 (mp3 |6|KB)1. Here is a cabinet under construction. The sides are all cut to the correct lengths, but the diagonals aren't equal. This means that the cabinet isn't square.

Can you answer? | Answer |
---|---|

Which top corner is less than 90°? | C |

Which top corner is greater than 90°? | A |

Which bottom corner is less than 90° ? | D |

Which bottom corner is greater than 90°? | B |

Which two corners does the cabinetmaker need to push towards each other to square up the cabinet? | C and D |

What length will both diagonals be when the cabinet is square? | 1570 |

2. A steel fabricator has a large off-cut of checker plate, and wants to know whether the top left hand corner is square. The sheet is 1500 mm wide, but its lengthwise dimensions vary because it has been cut on an angle.

The fabricator measures 2000 mm down on the left hand side and marks the point. He then measures between that mark and the top right hand point.

What length will this diagonal line be if the top left corner is square?

What length will this diagonal line be if the top left corner is square? | 2500 |