Question

what is the length of EF in the right triangle below?

Answer 1

Use the Pythagorean theorem:

$|DF|^2+|EF|^2=|DE|^2$

We have |DF| = 12 and |DE| = 19. Substitute:

$12^2+|EF|^2=19^2\\\\144+|EF|^2=361\qquad|-144\\\\|EF|^2=217\to|EF|=\sqrt{217}$

Answer: $C.\ \sqrt{217}$