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Pre-Calc Exam Notes 46

# Pre-Calc Exam Notes 46 - 46 Chapter 2 • General Triangles...

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Unformatted text preview: 46 Chapter 2 • General Triangles §2.2 The angle between two sides of a triangle is often called the included angle . Notice in the Law of Cosines that if two sides and their included angle are known (e.g. b , c , and A ), then we have a formula for the square of the third side. We will now solve the triangle from Example 2.4. Example 2.5 b = 4 a c = 5 A = 30 ◦ B C Case 3: Two sides and the angle between them. Solve the triangle △ ABC given A = 30 ◦ , b = 4, and c = 5. Solution: We will use the Law of Cosines to find a , use it again to find B , then use C = 180 ◦ − A − B . First, we have a 2 = b 2 + c 2 − 2 bc cos A = 4 2 + 5 2 − 2(4)(5) cos 30 ◦ = 6.36 ⇒ a = 2.52 . Now we use the formula for b 2 to find B : b 2 = c 2 + a 2 − 2 ca cos B ⇒ cos B = c 2 + a 2 − b 2 2 ca ⇒ cos B = 5 2 + (2.52) 2 − 4 2 2(5)(2.52) = 0.6091 ⇒ B = 52.5 ◦ Thus, C = 180 ◦ − A − B = 180 ◦ − 30 ◦ − 52.5 ◦ ⇒ C = 97.5 ◦ ....
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