Theta is the symbol used for the unknown angle in a triangle. When working with right angle triangles – triangles with one 90 degree angle – you can use Soh Cah Toa to help you find the unknown angle.

Before learning how to find the missing angle right away, there’s a few steps to understand.

First, label your triangle. This will let you know which Trigonometry function to use when calculating Θ.

There’s the hypotenuse – the longest length of the right angle triangle, the opposite – the angle opposite to the Θ or the angle you are looking for, and the last length left is called the adjacent.

In order to find Θ, you need to know at least two lengths.  This can help you apply Soh Cah Toa.

Soh Cah Toa is an acronym to help you find with trig function you should use in order to find Θ. The first letter of each three is the trig function; S = sine, C = Cosine, T = tangent. The next two letters are the side lengths and their order; o = opposite, a = adjacent, h = hypotenuse. So; Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

When you know two lengths and you know their side names, you can find the function you need to solve for Θ. For example, if you know the length of the opposite and hypotenuse, you can use sine to find the angle.

When solving for an angle, you use the inverse of the function.

sin(Θ)= 20/29 

Θ = sin^–1(20/29)

Θ = 44 degrees. (rounded to the nearest ten)

When finding a length when you know your angle, you can use one of the functions. For example if we know the opposite and the angle and are trying to find the hypotenuse, we can use sine again. x = the unknown length (hypotenuse)

sin(44 degrees) = 20/x

20 ÷ sin(44 degrees) = x

29 (rounded to the nearest ten) = x

–

I found trig to be a very easy subject of math. As long as you were able to identify the lengths of the triangle, there was an acronym to follow after and formulas that made finding the number simple.