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P1-26 Law of CoSines

P1-26 Law of CoSines. Given Irregular Quadrilateral By Law of CoSines. P1-26 Law of CoSines. Given Quantities  Find c 2 when Instructor to WhtBd to Build Quadratic Eqn in c 2. P1-26 Law of CoSines. Build Quadratic Eqn in c 2

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P1-26 Law of CoSines

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  1. P1-26 Law of CoSines • Given Irregular Quadrilateral • By Law of CoSines

  2. P1-26 Law of CoSines • Given Quantities  • Find c2 when • Instructor to WhtBd to Build Quadratic Eqn in c2

  3. P1-26 Law of CoSines • Build Quadratic Eqn in c2 • Instructor to Write m-file from Scratch (start w/ blank m-file)

  4. 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

  5. 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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