Solved: Law of Cosines All triangles satisfy the Law of
Chapter 12, Problem 71(choose chapter or problem)
Law of Cosines All triangles satisfy the Law of Cosines c2 = a2 + b2 - 2ab cos u (see figure). Notice that when u = p>2, the Law of Cosines becomes the Pythagorean Theorem. Consider all triangles with a fixed angle u = p>3, in which case c is a function of a and b, where a 7 0 and b 7 0. a c b _ a. Compute 0c 0a and 0c 0b by solving for c and differentiating. b. Compute 0c 0a and 0c 0b by implicit differentiation. Check for agreement with part (a). c. What relationship between a and b makes c an increasing function of a (for constant b)?
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