Trigonometry
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Trigonometry Reference Home Back to Thinkquest Contents
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Definitions of Trigonometric Functions Trigonometric Functions of Sums and Differences Inverse Trigonometric Functions
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Application Problem Given three sides of a triangle, find all the angles.
Solution: To find all the angles of the triangle, we can use the cosine law. CosA = (b2 + c2 - a2)/2bc CosA = (32 + 62 - 52)/2(3)(6) CosA = (9 + 36 -25)/36 CosA = 20/36 CosA = 0.5555 Use the inverse cosine function to find <A <A = 56.3° CosB = (a2 + c2 - b2)/2ac CosB = (52 + 62 - 32)/2(5)(6) CosB = (25 + 36 - 9)/60 CosB = 52/60 CosB = 0.86666 <B = 29.9° CosC = (a2 + b2 - c2)/2ab CosC = (52 + 32 - 62)/2(5)(3) CosC = (25 + 9 - 36)/30 CosC = -2/30 CosC = -0.06666 <C = 93.8° To check that we did it right, we can add up all our answers to see if we get 180°. 56.3° + 29.9° + 93.8° = 180° It checks, but if the result was close and off by less than 1 degree, that would be because we rounded the answers so they were not precise. In this case, it worked out great.
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