Question

已知三角形的三个内角之比是为5:6:7,三边之和为128,求三边的长?

Answer 1

三角形内角和为180,比例为5：6:7,则内角分别为50,60,70,根据正弦定律,令a/sin50=b/sin60=c/sin70=k,

a=k*sin50,b=k*sin60,c=k*sin70,

a+b+c=128

即k*(sin50+sin60+sin70)=128

k=128/(sin50+sin60+sin70)

=49.77

a=k*sin50

=38.13

b=k*sin60

=43.10

c=k*sin70

=46.77