Stitz-Zeager_College_Algebra_e-book

These equations enable us to easily convert points

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Unformatted text preview: , a = 7 units, c = 2 units 2. a = 4 units, b = 7 units, c = 5 units Solution. 1. We are given the lengths of two sides, a = 7 and c = 2, and the measure of the included angle, β = 50◦ , so the Law of Cosines applies.3 We get b2 = 72 + 22 − 2(7)(2) cos (50◦ ) which yields b = 53 − 28 cos (50◦ ) ≈ 5.92 units. In order to determine the measures of the remaining angles α and γ , we are forced to used the derived value for b. There are two ways to proceed at this point. We could use the Law of Cosines again, or, since we have the angle-side opposite pair (β, b) we could use the Law of Sines. We will discuss both strategies in turn. In either case, we follow the rule of thumb ‘Find the larger angle first.’4 Since a > c, this means α > γ , so we set about finding α first. If we choose the Law of Cosines route, it is helpful to rearrange the formulas given in Theorem 11.5. Solving a2 = b2 + c2 − 2bc cos(α) 2 c2 − 2 for cos(α) we get cos(α) = b +2bc a . Plugging in a = 7, b = 53 − 28 cos (50◦ ) and c = 2, we ...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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