The information given represents lengths of sides of a right triangle with c the hypotenuse. find the correct missing length to the nearest hundredth. a calculator may be .

a = ? , b = 11, c = 17

a.
12.96

b.
13.12

c.
13.20

d.
12.75

The sides of a right triangle can always be expressed as:

h^2=x^2+y^2, where h is the length of the hypotenuse and x and y are the side lengths.

If we are to assume that "a" is a side length then 17 or "c" must be the hypotenuse so:

17^2=11^2+a^2

a^2=289-121

a^2=168

a=√168

a≈12.96  (to nearest hundredth)

Note we knew this assumption because of the answer choices, but technically, "a" COULD have been the hypotenuse without this implicit suggestion making:

a^2=17^2+11^2

a^2=410

a=√410

a≈20.25 (to the nearest hundredth)

Of course the above is not relevant to this particular question but be aware that you won't always be given answer choices to make the assumption of which side is the hypotenuse...