Question

A right triangle. If AC = 7 and BC = 8, find AB. Leave your answer in simplest radical form.

Answer 1

We don't know whether those two sides are both legs
of the right triangle, or if  BC  is the hypotenuse.

If  AC  and  BC  are both legs, then

           AB = √ (AC² + BC²)
                 =  √ (7² + 8²)
                 =  √ (49 + 64)  =  √ 113 .

If  BC  is the hypotenuse of the right triangle, then

           AB = √ (BC² - AC²)
                 =  √ (8² - 7²)
                 =  √ (64 - 49)  =  √ 15 .