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