Question

What is the length of side AB if AC = 8 cm and BC = 15 cm?

Answer 1

Assuming we are dealing with a right-angled triangle,
there are two possible answers:
`abs(AB)=17color(white)("xxx")orcolor(white)("xxx")abs(AB)=sqrt(161)~~12.69`

Explanation:

Assuming a right angled triangle, we have one of 2 possibilities for the given values:

In either case we can use the Pythagorean Theorem to determine the length `abs(AB)`

#{: ("if "AB" is the hypotenuse",color(white)("xxx"),"if "AB" is not the hypotenuse"), (abs(AB)^2=abs(AC)^2+abs(BC)^2,,abs(AB)^2=abs(BC)^2-abs(AC)^2), (abs(AB)^2=8^2+15^2,,abs(AB)^2=15^2-8^2), (abs(AB)^2=64+225,,abs(AB)^2=225-64), (abs(AB)^2=289,,abs(AB)^2=161), (abs(AB)=sqrt(289)=17,,abs(AB)=sqrt(161)~~12.68857754) :}#