Soh-Cah-Toa, Law of Sines, Law of Cosines Objectives: Be able to state the Law of Cosines formula. Be apply to apply the Law of Sines on SAS triangles. Be apply to apply the Law of Sines on SSS triangles. Critical Vocabulary: Soh-Cah-Toa, Law of Sines, Law of Cosines

Law of Cosines Can we use the law of sines? When all else fails…use the Law of Cosines. Can we use the Pythagorean Theorem to find c? Can we use SOH-CAH-TOA? That’s great, but what is the Law of Cosines? No, we don’t know an angle and its opposite side. No, the triangle is not a right triangle. No, the triangle is not a right triangle.  c Directions: Find all the missing parts. 2  60 3 Law of Cosines

Let’s begin by finding “c” since this is a SAS triangle and I know the value of gamma. Don’t plug into your calculator until you get “c” all by itself. We now need to find alpha next because you ALWAYS need to find the largest angle last. Since the largest side is 3, that means beta is the largest angle. We will use the Law of Sines to find alpha. All that’s left to find is beta. Since we know the sum of the interior angles of a triangle is 180 degrees we can find this very easily.  2.65 c 79.2° 2  40.8° 60 3

We will use the Law of Cosines again to find beta since we can avoid a double rounding error. DO NOT use the Law of Sines, this will result in a possible double rounding error. We have choices here. We can find either alpha or beta first. Since the largest side is 6, we MUST find gamma last. Let’s find alpha first All that’s left to find is gamma. Since we know the sum of the interior angles of a triangle is 180 degrees we can find this very easily.  26.4° 6 4 117.3°   36.3° 3

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