In this lesson, we will learn all about the Law of Cosines.
The coolest thing about the formula is that it is just an extension of the Pythagorean Theorem, which means it is super easy to remember.
Law of Cosines Equation
Okay, so the first part is nothing more than the sum or the square of each side length, just like the Pythagorean Theorem.
The remaining portion of the equation is merely subtracting the product of twice two side lengths and an oblique angle.
And while it is true that there are three different versions of the Law of Cosines, you will only need to learn one of them, and then simply change the letters to find your needs.
Using the formula may sound complicated at first, but once you see it in action, you will love the simplicity of the Law of Cosines Equation.
The Formula for the Law of Cosines
In fact, as long as you know the first three letters of the alphabet and the Pythagorean Theorem, then you can be a Law of Cosines champion!
When do you use the Law of Cosines
We will always use it for any Oblique Triangles where we have Side-Angle-Side (SAS) or Side-Side-Side (SSS) congruency.
How do you use the Law of Cosines
- Draw and label a standard Oblique Triangle, as we’ve done in our previous lessons.
- Determine the given congruence, either SAS or SSS, and pick the equation that helps you solve for either a missing side or angle.
- Plug into your chosen equation and solve.
Additionally, as we will soon discover, this method is only necessary for completing our first step in solving these oblique triangles. After that we can fall back to the simplicity of the Law of Sines if we so desire, as HyperPhysics accurately states.
Together, we will see how it is derived and then walk through several examples together in detail.
Law of Cosines – Worksheet
- Law of Cosines Reference Sheet: This handout includes the Law of Cosines Formula, Steps for solving oblique triangles, and 2 practice problems with solutions.
Law of Cosines – Video
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