Question

The lengths of the sides of a triangular garden are 10m, 11m, and 13m. find the measure of the angle opposite the longest side to then nearest tenth of a degree

Answer 1

we know that
applying the law of cosines
c²=a²+b²-2*a*b*cos C

in this problem
a=10 m
b=11 m
c=13 m
C=?

c²=a²+b²-2*a*b*cos C----> cos C=[a²+b²-c²]/[2*a*b]
cos C=[10²+11²-13²]/[2*10*11]----> cos C=0.2364
C=arc cos (0.2364)----> C=76.33°

the answer is
76.3°