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Unit: Making measurements

Supporting: MSAPMOPS101A Make measurements

Section 2: Measuring

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When two straight lines meet, they form an angle between them.

If the lines are walls in a square room, or the sides of a square box, they will form a right angle.

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Another way of referring to a right angle is to say it is 90° (degrees).

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°.

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Setting out and checking angles

The most common hand-held tools used to set out angles are:

Carpenter's square, also called a framing square, because it is sometimes used to set out angles on roof framing timbers, such as rafters.

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Combination square, which allows you to set out 90° and 45° angles.

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Bevel, which lets you set any angle you like.

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Protractor, which is like a bevel but has the degrees marked in an arc.

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Electronic angle finder, which provides a digital readout of the angle formed by the arms.

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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.

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You can also use a level to check whether a surface or line is 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.

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The angle formed between a vertical line and a horizontal line is exactly 90°.

So there are many times, particularly in building projects, when you can check whether two surfaces form a right angle by simply using a level.

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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.

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If the diagonals are not the same length, then the corners can't be square, even if the sides are still parallel.

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.

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Using the 3, 4, 5 rule

Can you still check an angle for square using a tape measure if the object doesn't have opposite corners? The answer is yes - by using the 3, 4, 5 rule. This is an application of an old formula that Pythagoras, the ancient Greek philosopher, came up with over 2,500 years ago.

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Let's say you wanted to check whether the walls in the corner of a room were square, but it was a big open-plan room that didn't have opposite corners to measure.

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.

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Learning activity

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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.

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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
Audio 16 (mp3 |6|KB)

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?

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

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