In this geometry lesson, you’re going to learn all about SohCahToa. Show Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher) It’s probably one of the most famous math mnemonics alongside PEMDAS. And it’s an essential technique for your mathematical toolbelt. Let’s get to it! What Is SohCahToa?It’s a mnemonic device to help you remember the three basic trig ratios used to solve for missing sides and angles in a right triangle. It’s defined as:
We’ll dive further into the theory behind it in the video below, but essentially it’s taken from the AA Similarity Postulate that we learned about previously. It stated that the ratios of the lengths of two sides of similar right triangles are equal. Therefore, the sets of ratios depend only on the measure of the acute angle, not the size of the triangle.
Remember the three basic ratios are called Sine, Cosine, and Tangent, and they represent the foundational Trigonometric Ratios, after the Greek word for triangle measurement. And these trigonometric ratios allow us to find missing sides of a right triangle, as well as missing angles. How To Remember Trig Functions?So how do we remember these three trig ratios and use them to solve for missing sides and angles? First, we remember how the sides of a right triangle are labeled:
The opposite leg is opposite one of the acute angles, the adjacent leg is next to the acute angle, and the hypotenuse is opposite the right angle, as it’s the longest side, as noted by the University of Georgia. Right Triangle Diagram Then we use the mnemonic device we talk about earlier: SOHCAHTOA! SOH-CAH-TOA Chart An easy way to remember the order of Sin, Cos, and Tan is to use saying such as: Some Of Her Children Are Having Trouble Over Algebra If you can remember the order of the trigonometric functions, then a quicker saying would be: Oscar Had A Heap Of Apples Modifying our equations from earlier, we have:
There are many more fun sayings as well. Few Examples…Given the following right triangle, solve for the missing side length, r: Using Sin to Find the Hypotenuse Sometimes we are given two sides lengths, and we need to determine one of the acute angles of the right triangle. How can we do this? Inverse Trig Ratios allow us to solve for those missing angles quite easily. Consequently, SOHCAHTOA is very versatile as it grants us the ability to solve for sides and angles of a right triangle! Inverse Trig Values In the next example we are asked to “Solve the triangle.” This means we are to solve for all missing side lengths and angle measurements. Finding Sides and Angles Using Inverse Trig Common QuestionsQ: Is sohcahtoa only for right triangles? Q: When to use sohcahtoa? Q: Where is the hypotenuse of a right triangle? Q: Where is the adjacent side of a triangle? Q: What does it mean to
solve a right triangle? In the video below, you’ll progress through harder examples involving trig ratios, calculating missing side lengths and angles, inverse trig, and much more! Video – Lesson & Examples1 hr 34 min
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