This week our subject was on trigonometry and more specifically this day was focused on finding the missing angles of a right angle (90 Degree) triangle. This missing angle was called “Theta” and could be found using SOH CAH TOA.

SOH CAH TOA is an acronym that will assist in helping to find the required trig function on a scientific calculator. The first letters of each term represents S = Sine, C = Cosine, T = Tangent. The next letters following show which side lengths are used for the function, O = Opposite, A = Adjacent, H = Hypotenuse.

To find the angle start by labeling each side of the triangle, this simplifies the task of remembering which side to use in the equations. The longest length would be the hypotenuse, the opposite would be the side opposite of Θ, and the last length right beside Θ would be the adjacent.

To find Θ it is required you know a minimum of two lengths of the triangle, with this you can apply SOH CAH TOA. For example knowing the length of the hypotenuse and the opposite you can use Sine to find Θ.

 

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

sin(Θ)= 8/12

Θ = sin–1(8/12)

Θ = 42 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(42 degrees) = 8/x

8 ÷ sin(42 degrees) = x

12 (rounded to the nearest ten) = x