SOH CAH TOA, for those who didn't take trig, is the acronym to remember how to solve right triangles. In any problem involving right triangles, you will generally have at least three pieces of information about the triangle, as in two angles and the length of the side between them, the length of two sides and the angle between them, etc. and with that info you can find all the angles (you only have to find two, come on, it's a right triangle so you KNOW right off the bat that one angle is 90 degrees, right>>>??!! ) and the length of the two sides and the hypotenuse (the longest side is called the hypotenuse).

SOH stands for Sine equals the Opposite Side Divided by the Hypotenuse.

So if you know the degrees in an angle of a right triangle, you can look up the sine of that angle, and then the sine of the angle will be equal to the length of the side OPPOSITE the angle , divided by the length of the Hypotenuse. So you can find the angle if you know the length of the opposite side (the one that faces the angle) and the hypotenuse. Or you can find the length of either the opposite side or the hypotenuse if you know the angle and it's sine, and the missing side from the SOH equation.

CAH stands for Cosine equals the ADJACENT Side length divided by the length of the Hypotenuse, so you can solve this one the same as you do the Sine one, but by using the lengths of the Adjacent side (one end of the side touches the angle, and forms one side of the angle) and the Hypotenuse, or as with the Sine, you could find the angle if you know the length of the Adjacent side and the hypotenuse, or find the length of either of those two sides if you know the other side from the CAH equation and the angle.

TOA stands for Tangent equals the Opposite Side divided by the Adjacent side and works just like the two above, given any two parts of the equation you can solve for the third part.

And once you have two sides of the triangle, of course you can solve for the length of the third side using the old Pythagorean Formula of

A (squared) plus B (squared) equals C(squared) or as it is usually written A²+B²=C², where A and B are the two sides of the right triangle which meet to form the 90 degree right angle, and C is the hypotenuse, which is the longest side, and is opposite the Right Angle.

That's your Trig lesson for today, Trig is one of the most useful forms of math for a machinist, and can be used to solve many problems in machining in the shop, and in carpentry, etc.