FORMULA SHELF
12 of 370
The arithmetic behind the work: what to measure, what to type in, and what the answer comes out as. Every formula says what the symbols mean and gives a worked example, so you can check it against a job you have already done.
SHELVES
Trigonometry
12 formulas
The 3-4-5 rule for square corners, diagonal braces and roof lengths.
Rise 3 m, run 4 m: the brace is 5 m.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Working out a ramp, roof pitch or the slope to a drain from two measurements.
A 1 m rise over 4 m run is 14 degrees.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Converting a survey line into a bearing. Adjust to 0-360 degrees.
dE 3 m, dN 4 m gives a bearing of 36.9 degrees.
Setting out a curved gate, an arch or a circular saw cut.
A 2 m radius and 60 degrees gives a 2 m chord.
Convenience only. Double-check the result against the worked example or a second method before you use it.
The third side of any triangle when two sides and the included angle are known.
Sides 5 m and 7 m with 60 degrees between them give 6.25 m.
Any calculation that uses angles in code, physics or engineering formulas.
180 degrees = 3.1416 radians.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Checking a survey, setting out a fence or measuring between two points on a plan.
(1,2) to (4,6) is 5 m.
Finding the centre of a span, a gate opening or a surveyed line.
(2,4) and (8,10) have midpoint (5,7).
Turning a calculator or spreadsheet result back into an angle you can set out.
1 radian = 57.3 degrees.
Convenience only. Double-check the result against the worked example or a second method before you use it.
Roof pitches, ramps, braces and setting out any right-angle triangle.
A 10 m rafter at 30 degrees rises 5 m.
Solving any triangle when you know an angle and its opposite side. Surveying and roof framing.
a = 5 m, A = 30 degrees, B = 60 degrees gives b = 8.66 m.
Odd-shaped plots and roof panels where the height is awkward to measure.
Sides 6 m and 8 m with 30 degrees between them = 12 m2.
Convenience only. Double-check the result against the worked example or a second method before you use it.
SOURCES & PROVENANCE
1 listed
This page is an AI-organised index. The label means the grouping and cross-links were compiled with AI; the information itself comes from the public-domain books, reports and manuals listed below. Open any source to read the local copy or follow the link to the original publication.