Question

Triangle ABC is a right triangle. if AC =7 and BC= 8 find AB. Leave your answer in simplest radical form.

Answer 1

Use the Pythagorean Theorem: $a^2+b^2=c^2$ where  a  and  b  are the legs of the right triangle, and  c  is the hypotenuse (longest side!).

There is no picture provided with the problem, so it might be possible for the right angle to be at C and the hypotenuse is AB.  But that won't work with the answer choices given, because then $(AB)^2=7^2+8^2 \\ (AB)^2=49+64=113 \\ AB = \sqrt{113}$

Now you know that the 7 must be a leg and 8 the hypotenuse.  Then $7^2+(AB)^2=8^2 \\ 49+(AB)^2=64 \\(AB)^2=64-49 \\ AB=\sqrt{15}$.

By the way, it cannot be that 7 is the hypotenuse because it's the longest side and 8 is longer.