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Unformatted text preview: ) get cos(α) = √2−7 cos(50 ◦ . Since α is an angle in a triangle, we know the radian measure 53−28 cos(50 ) of α must lie between 0 and π radians. This matches the range of the arccosine function, so 2 This shouldn’t come as too much of a shock. All of the theorems in Trigonometry can ultimately be traced back to the definition of the circular functions along with the distance formula and hence, the Pythagorean Theorem. 3 There is no way to obtain an angle-side opposite pair, so the Law of Sines cannot be used at this point. 4 If you go the Law of Sines route, this can help avoid needless ambiguity. 11.3 The Law of Cosines we have α = arccos 775 ◦) 53−28 cos(50◦ ) √2−7 cos(50 radians ≈ 114.99◦ . At this point, we could trust our approximation for α and find γ using γ = 180◦ − α − β ≈ 180◦ − 114.99◦ − 50◦ = 15.01◦ . If we want to minimize propagation of error, however, we could run through the Law of Cosines 2 2 2 again,5 in this case using cos(γ ) = a +bab−c . Plugging in a = 7, b = 53 − 28 cos (50◦ ) a...
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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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