## Calculated Lengths

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### Drawing Right Triangles Using Calculated Lengths

Probably the most frequent means of drawing a right triangle is when the length of the sides of the right triangle have been calculated, and those dimensions are used to lay out the triangle.

For instance, you know a 45° right triangle with a leg length of 4" is needed. You also know that the legs of a 45° right triangle are perpendicular and are equal in length.

This knowledge is used in drawing that triangle.

First: Use a framing square or a compass to draw perpendicular lines.

Second: Set the dimension of your compass for 4" and mark both lines from the vertex of the 90° angle.

Third: Connect the points and you will have drawn a 45° right triangle.

For any right triangle, if you know the lengths of the legs, you can draw perpendicular lines, measure and mark the needed distance for each leg from the vertex of the angle, and connect the marks.

Example: Draw a 26.5° right triangle with an opposite side length of 6".

In order to draw this triangle, the length of the adjacent side needs to be known.

A look at the NAK chart shows that if your knowns are an angle and the length of the opposite side and your need is the length of the adjacent side, the cotangent function is used for your calculation.
```Cot 26.5°  x the length of the opposite side = The length of the adjacent side
Cot 26.5°  x 6" = The length of the adjacent side
2.006 x 6" = The length of the adjacent side
12.036" or 12 1/32" = The length of the adjacent side```
Second: Draw perpendicular lines using a compass or a framing square.

Third: Measure and mark 12 1/32" from the vertex of the angle on the horizontal line and 6" on the vertical line.

Fourth: Connect the two marks.

Protractors don't generally offer a high degrees of accuracy. If accuracy in your work is critical, then the ability to calculate and mark lengths for the sides of right triangles is also critical. For instance, if the length of the adjacent side was 12" instead of 12 1/32". the angle would be 26.6° .

For some of our work, a tenth of a degree makes little difference, but in other cases it does. Be aware and make calculations based on the accuracy needed for your work.

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