The distance from Joville to Precalctown is 675 kilometers f

The distance from Joville to Precalctown is 675 kilometers, from Precalctown to Mathmagic Land 800 kilometers, and from Mathmagic Land to Joville 725 kilometers. What are the angles in the triangle with these three cities as vertices?

Solution

Use cosine rule a=675, b=800,c=725

c^2=a^2+b^2-2abcosC

2abcosC=a^2+b^2-c^2

2×675×800cosC=675^2+800^2-725^2

CosC=.527

C=58.1degree

Sine rule

a/sinA=b/sinB=c/sinC

675/sinA=725/sin58.1

SinA=0.782

A=51.4degree

B=180-(A+C)

B=180-(58.1+51.4)

B=70.5degree