For this problem my method of estimating is accurate. This is because the sine and tangent of a very small angle is almost equal to the angle itself. This is true for 2 decimal places up to about 15 degrees and to three decimal places at 10 degrees or less. If you need exact results you need to use a calculator or published tables with values out to 8 decimal places or beyond. Just a question of how exact you want and need to be.
Measure it with a micrometer, mark it with a piece of chalk and cut it with an axe. Decide how accurate YOU need to be.