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ENGR-25_Prob_9_3_Solution.ppt 1 Bruce Mayer, PE Engineering-25: Computational Methods P1-26 Law of CoSines Given Irregular Quadrilateral By Law of CoSines

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ENGR-25_Prob_9_3_Solution.ppt 2 Bruce Mayer, PE Engineering-25: Computational Methods P1-26 Law of CoSines Given Quantities Find c 2 when Instructor to WhtBd to Build Quadratic Eqn in c 2 b 1 = 180 mc 1 = 115 mA 1 = 120° b 2 = 165 mA 2 = 100°

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ENGR-25_Prob_9_3_Solution.ppt 3 Bruce Mayer, PE Engineering-25: Computational Methods P1-26 Law of CoSines Build Quadratic Eqn in c 2 Instructor to Write m-file from Scratch (start w/ blank m-file)

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ENGR-25_Prob_9_3_Solution.ppt 4 Bruce Mayer, PE Engineering-25: Computational Methods P1-26 mFile & Results % Bruce Mayer, PE % EGNR25 * 23Jun11 % file = P1_26_LawOfCos_1106.m % % Set Known ParaMeters b1 = 180; b2 = 165; c1 = 115; % all in meters A1 = 120; A2 = 100; % all in Degrees % % Calc the constant a^2 asq = b1^2 + c1^2 -2*b1*c1*cosd(A1) % note use of cosd % % Make Quadratic PolyNomial c2Poly = [1, -2*b2*cosd(A2), (b2^2 - asq)] % % Find roots of PolyNomial c2roots = roots(c2Poly) % % NOTE: since c2 is a DISTANCE it MUST be POSITIVE asq = 66325 c2Poly = 1.0e+004 * 0.0001 0.0057 -3.9100 c2roots = -228.4542 171.1503 ANSWER

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ENGR-25_Prob_9_3_Solution.ppt 5 Bruce Mayer, PE Engineering-25: Computational Methods Another Solution % Bruce Mayer, PE % 20Aug12 * ENGR25 % file P1_26_LawOfCos_Alternative_1208.m % % Side Lengths in meters b1 = 180, b2 = 165, c1 = 115 % commas do NOT suppress ReadBack % % Angles in Degrees A1 = 120; A2 = 100; % semicolons DO suppress ReadBack % % calc parameter "asqd" asqd = b1^2 + c1^2 - 2*b1*c1*cosd(A1) % note use of cosd; not cos. cos operates on radians % c2QuadCoeff = [1 -2*b2*cosd(A2) b2^2-asqd] % find Roots of Quadratic c2 = roots(c2QuadCoeff) % Note that c2 is a DISTANCE and hence MUST be POSITIVE

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