methods
Other Triangles
If circumstances warrant it, there are other combinations of integers that can be used to obtain a right angle triangle. They include: 5/12/13, 8/15/17, 10/24/26, 5/5/7.07, 10/10/14.14, etc. Undoubtedly, there are many more that could be used.
The Pythagorean Theorem
If the field engineer wants to be able to use any distances to lay out or check a right angle, the Pythagorean Theorem is the tool to use. If the sides of a building are 26.5 and 32.5, inputting these numbers into the Pythagorean formula will yield a hypotenuse of 41.93. The field engineer can use this distance to be sure a right angle exists. Recall:
3/4/5 Requirements
Using the 3/4/5 is a very simple process, however, to achieve the expected results, the measurements must be exact. That is, follow proper chaining techniques carefully. Any error in the measurement of the distances will result in not establishing a right angle as desired. Or if an established 90° angle is being checked, inaccurate measurement may cause the field engineer to make an adjustment that is unnecessary.
If using the 30/40/50-feet triangle, calculations show that being off just 0.01 in the measurement of the 50' hypotenuse results in an angular error of over two minutes of arc. In other words, the planned right angle will be 89°58' or 90°02' depending on whether the distance is 49.99 or 50.01. If shorter distances such as 3, 4, and 5 feet are used, an error of 0.01 when measuring the 5 foot hypotenuse results in an angular error of almost 15 minutes! It cannot be stressed enough that exact measurements are necessary to obtain desired results when using the 3/4/5 method of laying out or checking a 90° angle.
Common Uses of the 3/4/5
The field engineer can use the 3/4/5 anytime a 90° angle is to be laid out or a 90° angle is being checked.
With Pythagorean, any triangle can be used.