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Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 852.
Let BC=a, CA=b, AB=c, Area of ΔABC = S. Then a=x+3, b=7, c=x+4, s=1/2(a+b+c)=x+7S = √[12x(x+7)] = 2(x+7)12x(x+7) = 4(x+7)^2x = 7/2
half of angle A = Arctan(2/4)and half of angle B = arctan(2/3)double these and subtract from 180 to find angle B. Then tan(B/2) = 2/x or2/tan(B/2) = x = 3.5Not as elegant as the solution above with more rounding involved. But fewer calculations.
Sorry, the first line should read:half of angle A = Arctan(2/4)and half of angle C = arctan(2/3)