Triangle ABC is a right triangle. if AC =7 and BC= 8 find AB. Leave your answer in simplest radical form. A : √(19) B : √(21) C : √(15) D : √(17)

Question

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

A :

`√(19)`
B :

`√(21)`
C :

`√(15)`
D :

`√(17)`

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 = √(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=√(15)`.

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