Question

prove that a triangle which has one of the angle 30°, cannot have all vertices with integral coordinates

Answer 1

Answer:

Step-by-step explanation:

Without loss of generality we can chose the co-ordinates ( we can make this by proper shift of co-ordinates) as A= (0,0), B= (x,y), C=(a,b)

Now slope of AB = y/x is rationalSlope of AC = b/a is rational

So tan (BAC) = ((y/x) – (a/b))/ ( 1 + ay/(bx)) which is rationsl

As tan 60 = sqrt(3) there cannot be any point with rational coefficient so angle BAC cannot be 60 degreeAs we cannot find any rational point on the kline at 60 degrees so getting an equilateral triangle is not possibleHence proved