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\( A = \cos^{-1} \left[ \dfrac{b^2+c^2-a^2}{2bc} \right]\) A = angle A B = angle B C = angle C a = side a b = side b c = side c P = perimeter s = semi-perimeter K = area r = radius of inscribed circle R = radius of circumscribed circle *Length units are for your reference-only since the value of the resulting lengths will always be the same no matter what the units are. Calculator UseUses the law of cosines to calculate unknown angles or sides of a triangle. In order to calculate the unknown values you must enter 3 known values. To calculate any angle, A, B or C, enter 3 side lengths a, b and c. This is the same calculation as Side-Side-Side (SSS) Theorem. To calculate side a for example, enter the opposite angle A and the two other adjacent sides b and c. Using different forms of the law of cosines we can calculate all of the other unknown angles or sides. This is the same calculation as Side-Angle-Side (SAS) Theorem.
Law of CosinesIf a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states: \( a^2 = b^2 + c^2 - 2bc \cos A \) \( b^2 = a^2 + c^2 - 2ac \cos B \) \( c^2 = a^2 + b^2 - 2ab \cos C \) Law of Cosines solving for sides a, b, and c\( a = \sqrt{b^2 + c^2 - 2bc \cos A } \) \( b = \sqrt{a^2 + c^2 - 2ac \cos B } \) \( c = \sqrt{a^2 + b^2 - 2ab \cos C } \) Law of Cosines solving for angles A, B, and C\( A = \cos^{-1} \left[ \dfrac{b^2+c^2-a^2}{2bc} \right] \) \( B = \cos^{-1} \left[ \dfrac{a^2+c^2-b^2}{2ac} \right] \) \( C = \cos^{-1} \left[ \dfrac{a^2+b^2-c^2}{2ab} \right] \) Triangle CharacteristicsTriangle perimeter, P = a + b + c Triangle semi-perimeter, s = 0.5 * (a + b + c) Triangle area, K = √[ s*(s-a)*(s-b)*(s-c)] Radius of inscribed circle in the triangle, r = √[ (s-a)*(s-b)*(s-c) / s ] Radius of circumscribed circle around triangle, R = (abc) / (4K) References/ Further ReadingWeisstein, Eric W. "Law of Cosines" From MathWorld-- A Wolfram Web Resource. Law of Cosines. Zwillinger, Daniel (Editor-in-Chief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 512, 2003. http://hyperphysics.phy-astr.gsu.edu/hbase/lcos.html http://hyperphysics.phy-astr.gsu.edu/hbase/lsin.html
Answer: IT ALREADY HAS SOLUTION HOPE IT HELPS(BRAINLIEST IF IT HELPS YOU) CORRECT ME IF IM WRONG:)Step-by-step explanation: #CARRYONLEARNING |