Problema Solution

In ∆ABC, if the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively, what are m B and m C to two decimal places?

Answer provided by our tutors

Use the law of cosines to find the angles:


a^2+b^2−2ab(cos mC)=c^2


cos mC = (a^2 + b^2 - c^2)/(2ab)


cos mC = (22.5^2 + 18^2 - 13.6^2)/(2*22.5*18)


cos mC = 0.796654321


mC = arccos 0.796654321


mC = 37.19 degrees


a^2+c^2−2ac(cos mB)=b^2


cos mB = (a^2 + c^2 - b^2)/(2ac)


cos mB = (22.5^2 + 13.6^2 - 18^2)/(2*22.5*13.6)


cos mB = 0.60001634


mB = 53.13 degrees