We can find the right angle of the triangle by finding the slope of the sides .
Any right angle makes an angle of 90 degrees and the lines are perpendicular .
For perpendicular lines product of slopes is -1.
In other words the slopes have opposite signs and are reciprocal .
Let us find the slopes of AB,BC,CA.
Slope of two points can be found by the difference in y values divided by different in x values
Slope of AB=
Slope of BC=
Slope of CA=
The slopes of AB and CA are reciprocal of each other with opposite signs or we can say their product is -1 so they are perpendicular.
Angle A is the common angle to these sides so we say angle A is the right angle