# SETTING-OUT A RIGHT-ANGLE USING THE 3:4:5 METHOD

The majority of buildings and structures are based around straight lines, squares and rectangles, meaning that most corners and junctions will be at right angles. The ability to set-out a right-angle correctly is, therefore, of fundamental importance since a rectangle or square, without care and attention, can easily become a rhombus shape.

A quick method of establishing a right-angle is to use a ‘long-arm’ version of a wooden builder’s square. As it is made from three separate pieces of timber, the accuracy of a timber square is only as good as the quality of its ‘manufacture’. Moreover, with use and exposure to weather, a timber builder’s square can warp. It may also come loose at the joints, which will further compromise accuracy.

The 3:4:5 method is a reliable alternative for setting-out and checking right-angles, enabling the front and back walls of the building to be set-out from side wall line ‘A’-‘B’. This will always give a perfect and accurate right-angle. The 3:4:5 method is based on Pythagoras’ Theorum, which states that for every right-angled triangle the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In other words, A + B = C (see Fig 53). A right-angled triangle with short sides of 3 units and 4 units will always have a longest side (hypotenuse) of 5 units. This simple ratio of 3:4:5 can be applied for the setting-out of any right-angle – all that is required is that the measurements used are in a ratio of 3:4:5, for example, a triangle with sides 600mm by 800mm by 1000mm, or (3 x 200mm) by (4 x 200mm) by (5 x 200mm).

For a practical application of this method for the front wall line of the garage, see Fig 54. The two string-lines are marked at 3 units and 4 units respectively by measuring out from corner peg ‘A’. The distance on the diagonal (hypotenuse) between marked points ‘X’ and ‘Y’ should measure 5 units. If not, peg ‘D’ and the line attached to it should be moved until there is an exact measurement of 5 units between ‘X’ and ‘Y’, which confirms that the angle at corner peg ‘A’ (in other words,

the angle formed between lines ‘A’-‘B’ and ‘A’-‘D’) is 90 degrees.

 Fig. 53 Pythagoras’ Theorem as the basis for the 3:4:5 method of setting-out a right-angle.

Fig. 54 Practical application of the 3:4:5 method to set-out a right-angle.