The hypotenuse is the longest side of the triangle. Side AC of the triangle is its hypotenuse, thus greater than BC (segment and angle theorem of a triangle).
A triangle is a shape with three side and angles. Its longest side is referred to as hypotenuse. And this side is usually opposite to the greatest angle. Examples of triangle include: equilateral, isosceles, acute, right angles, obtuse angle etc.
The given question shows that triangle ACB is a right angled triangle. This is because <CBY = [tex]90^{o}[/tex].
So that;
<CBY + <CBA = [tex]180^{o}[/tex]
Now comparing side AC with BC:
The segment and angle theorem of a triangle states that: the longest side of a triangle is always opposite to the greatest angle.
Thus, since <CBA is the greatest of the angles here, then AC is the longest side.
Therefore, the side AC is the hypotenuse of the triangle and it is greater than BC.
A sketch to this question is attached to this answer for more clarifications.
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