Properties Of Triangles

In any triangle ABC

In any triangle ABC: a/sin A = b/sin B = c/sin C = 2R, where R is circumradius. This means the ratio of each side to sine of its opposite angle is con

Three formulas

Three formulas: a² = b² + c² - 2bc cos A, b² = c² + a² - 2ca cos B, c² = a² + b² - 2ab cos C. Also: cos A = (b² + c² - a²)/(2bc). STEP-BY-STEP APPLICA

Three formulas

Three formulas: a = b cos C + c cos B, b = c cos A + a cos C, c = a cos B + b cos A. Each side equals sum of projections of other two sides. STEP-BY-S

Key formulas

Key formulas: sin(A/2) = √[(s-b)(s-c)/(bc)], cos(A/2) = √[s(s-a)/(bc)], tan(A/2) = √[(s-b)(s-c)/(s(s-a))], where s = (a+b+c)/2. STEP-BY-STEP APPLICATI

Area = √[s(s

Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 is semi-perimeter. STEP-BY-STEP CALCULATION: (1) Find semi-perimeter s (2) Calculate s-a, s-b, s-c (3)