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Solving Triangles University of Minnesota Solving Triangles Preliminaries and Objectives Preliminaries: • Law of Sines • Law of Cosines Objectives: • Given three parts of a triangle, find the missing three parts. University of Minnesota Solving Triangles AAA B 72◦ 63◦ 45◦ A C University of Minnesota Solving Triangles AAA B 72◦ 63◦ 45◦ A C University of Minnesota Solving Triangles AAA B 72◦ 63◦ 45◦ A C University of Minnesota Solving Triangles ASA or ASA Given two angles and one side • Find the third angle by adding to 180◦ • Find a second side using the Law of Sines. You will get the correct approximate answer from your calculator. • Find the third side using the Law of Sines. Beware of using a rounded off answer to find a second rounded off answer. The rounding errors will compound. University of Minnesota Solving Triangles SAS B c=3 32◦ a=8 A C b2 = 32 + 82 − 2(3)(8) cos 32◦ ≈ 32.294 ⇒ b ≈ 5.683 University of Minnesota Solving Triangles SAS B c=3 A 32◦ a=8 b ≈ 5.683 C sin A sin 32◦ = ⇒ sin A ≈ .74600 8 5.683 sin−1 0.74600 ≈ 48.2◦ University of Minnesota Solving Triangles SAS B c=3 A 32◦ a=8 b ≈ 5.683 C sin C sin 32◦ = ⇒ sin C ≈ .27975 3 5.683 ⇒ C ≈ 16.2◦ ⇒ A ≈ 131.8◦ University of Minnesota Solving Triangles SSA Given two sides and an angle opposite one of the two sides • Try to find the angle opposite the second side by using the Law of Sines. If you are taking the inverse sine of a number bigger than 1, you will get no solution, otherwise • Your calculator will give you one possible angle θ, the second possible angle is 180◦ − θ. • Find the third angle. If the sum of the first two angles is more than 180◦ , then there will only be one solution. • Find the third side of all possible triangles using the Law of Sines. University of Minnesota Solving Triangles SSS B c=3 A a=8 b=6 C 82 = 32 + 62 − 2(3)(6) cos A ⇒ cos A = − ⇒ A ≈ 121.9◦ B ≈ 39.5◦ University of Minnesota Solving Triangles 19 36 C ≈ 18.6◦ Credits Written by: Mike Weimerskirch Narration: Mike Weimerskirch Graphic Design: Mike Weimerskirch University of Minnesota Solving Triangles Copyright Info c The Regents of the University of Minnesota & Mike Weimerskirch For a license please contact http://z.umn.edu/otc University of Minnesota Solving Triangles
