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# Lay out an angle using the chordal method

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Lay out large angles accurately.
Useful for Fabrication/Boilermaking.

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### Lay out an angle using the chordal method

1. 1. The chord of a circle is a straight line joining any two points on its circumference.
2. 2. 1000 45° 765.4 A B C The Chord length of 45° is 0.7654
3. 3. 1000 45° 765.4 A B C Draw lineA-B at 1000 units. This is our scale factor. Values are derived from the Unit Circle.
4. 4. 1000 45° 765.4 A B C Using the measurementA – B (as radius) and pivot pointA produce an arc.
5. 5. 1000 45° 765.4 A B C From point B produce an arc equal to 1000 times the value obtained from aTable of Chords relative to the required angle. 0.7654 multiplied by 1000 = 765.4
6. 6. 1000 45° 765.4 A B C Mark the intersection of the two arcs ©. Draw a line from the pivot A through point C. The angle BAC is the required angle.
7. 7. 1000 45° 765.4 A B C If aTable of Chords is unavailable, obtain the chordal value from a scientific calculator using the following method. If the required angle is 45° then : sin 45deg 2       2 0.7654 T
8. 8. 1 UNIT A B C 22.5° 0.3826 0.7654 The Unit Circle The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse, which in the example below is one unit. The sine of an angle is equal to half the chord of twice the angle. sin ( ) opposite hypotenuse  Sin (22.5 deg) = 0.38268 0.38268 x 2 = 0.7654