given: abc with ab=c, bc=a, ac=b. prove: a/sinA =b=sin B=c/sin c

Question

answers could be:

a)definition of cosine in right triangle

b)definition of sine in right triangle

c)definition of tangent in right triangle

d)corresponding sides of congruent triangles are equal

e)definition of equilateral triangle

Answer 1

each side is equal

a=b=c = 1

it's an equilateral triangle with all sides equal and all angles equal

each angle is equal = 180/3 = 60 degrees = pi/3

A=B=C = 60 degrees = pi/3 radians

a/sinA = b/sinB = c/sinC = 1/sqr3/2= 2/sqr3 = (2/3)sqr3

just solve any of the 3 equations for a, b or c, substitute into the other equations, and you get a=1, b=1 and c=1