Question 1129618
Is this with compass and straightedge alone?
If so, then:
(1) draw a straight line
(2) construct a perpendicular to the line at point A
(3) bisect one of the 90 degree angles formed
(4) lay out 13 units on this bisector ( any units )
Call the end of this line segment B
(5) drop a perpendicular from B
to the original line. call the intersection C
(6) the line segment AC is {{{ sqrt(13 ) }}} units long