With the April ACT coming up, now is a great time to make sure you know some of the math concepts that have been coming up regularly on exams. One of these is application of your trig functions. SOHCAHTOA is a great mnemonic for remembering the side relationships of sine, cosine, and tangent (in terms of adjacent, opposite, and hypotenuse of a right triangle).
Here’s how it typically appears on the ACT: You are given two sides of a triangle (perhaps in the context of a shape such as a garden, or a person looking up at the top of a tree) and must find one of the angles. Alternatively, you could be given an angle and one side and asked to find other sides. If the angles are anything other than 30, 45, or 60 degrees, the ACT will either leave answers in terms of trig functions (or inverse trig functions) or give you the trig values for the angles in question.
When dealing with a question like this, always draw out your triangle. Label the information that you know (any side lengths and angles). Mark what you need to find. Then, look at the relationship between the angle that you are given or need to find and the side lengths. Choose the appropriate trig function and set up your question (e.g., sine x = opposite/hypotenuse, but now substituting in two of the three pieces of information that you know). Solve for the unknown, and you’re done!
