Question

The sides of a triangle have side lengths equal to a,b and√ (a^2−ab+b^2). What is the measure of the angle (in degrees) between the longest and shortest side?

Answer 1

a>b or b>a? This is quite important?

Answer 2

you can assume

Answer 3

If a>b then,
b<√ (a^2−ab+b^2) <a
If b>a then,
a<√ (a^2−ab+b^2) <b
Now,
let the angle be x then,
( √ (a^2−ab+b^2))^2 = a^2+b2-2ab cosx
a^2 -ab +b^2=a^2+b^2-2ab cosx
cosx=1/2
x=60