Question

A tree one hundred cubits high is distant from a well two hundred cubits; from this tree one monkey climbs dow the tree and goes to the well, but the other leaps in the air and descends by the hypotenuse from the high point of the leap, and both pass over an equal space. Find the height of the leap.

Answer 1

I assume you mean the monkey leaped straight up. Ignoring the fact that free-fall trajectories are parabolas, and not straight lines, we have

x = height of leap
300 = hypotenuse
(because the distance down the tree and over to the well is 300)

√(200^2 + (100+x)^2) = 300
x = 100(√5 - 1) = 123 cubits.

That's some leap!!