Bella: Really? That's so cool, what is SOH CAH TOA and how can I do that?
Bella: Check out that new building! I wonder how tall it is!
Vincent: You can find out what it is using SOH CAH TOA, Bella. I learned it in math class today!
Vincent: Well, first you have to know what SOH CAH TOA stands for. It's ratios for trigonometry functions which are Sine, Cosine, and Tangent. The acronym SOH CAH TOA helps you remember their formulas. For Sin, its opposite over hypotenuse, Cos is adjacent over hypotenuse, and Tan is opposite over adjacent.
Bella: What are the opposite, hypotenuse and adjacent in a triangle?
Vincent: They're used to calculate the unknown side lengths and angles in right angle triangles.
Bella: What are these ratios used for?
Vincent: Well, that depends on which angle we are focusing on, which is called the reference angle. The hypotenuse is always the longest side of the right triangle, the adjacent is the side closest to the reference angle, and the opposite is the side furthest/opposite from the reference angle.
Bella: Oh, okay I'm starting to understand now!
Vincent: The reference angle is also always an acute angle, which means that it is less than 90 degrees.
Bella: That makes it easier to understand, Thanks Vincent.
Vincent: No problem!
Vincent: Here's an example:
opposite
adjacent
hypotenuse
angle
Bella: Oh, that makes sense!
Vincent: Also, if you want to find only the angle from the given side lengths, for example for Sinθ, then you use the inverse function of Sin-1 to find it. This inverse takes the Sine ratio of opposite/ hypotenuse and uses it to find the angle θ.
Bella: When it's about side lengths, can't we use the Pythagorean theorem for right angle triangles?
Vincent: Not in all cases, because sometimes we don't have two side lengths to determine the third one, so we use an angle and a side or any other two components with SOHCAHTOA to solve for the side length.