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Q8: How does the law of cosines work?
My teacher wants me to find the sides of a triangle, but it's not a right triangle. I know two sides and one of the angles. How can I find the third side without using the Pythagorean Theorem?
You're right -- the Pythagorean Theorem doesn't apply here because it's not a right triangle. Instead, we can use the Law of Cosines to find the missing side:
The Law of Cosines is really a generalized version of the Pythagorean Theorem. If it's a right triangle then the angle C is 90 degrees, so its cosine is 0. Plug that into the above equation and the whole extra term disappears.
In this case the angle C is 30 degrees, and a is 3 and b is 4. You'll notice that it doesn't matter which we call a or b.
Of course, if it was a regular right triangle we know that the length of side C would have been 5. In this case, the length is just 2.05 because the angle is a lot smaller.