# Question #0ea77

Jan 20, 2018

Knowing the leg with length $10$ is the hypotenuse, then yes, it is as you put it.

#### Explanation:

If $a$ is the hypotenuse (longest leg, opposite the right angle) of a right triangle, for the lengths of the other two legs, the pythagorean theorem states that ${a}^{2} = {b}^{2} + {c}^{2}$. In your case, the most likely answer is that the remaining leg is $6$, as you described.

But there's a chance the remaining leg is actually the hypotenuse (if not already specified of course) in which case we would have that

$x = \sqrt{{10}^{2} + {8}^{2}} = \sqrt{164} = 2 \sqrt{41}$

Don't let the above bother you as much, there's probably an implication somewhere in the problem that the leg of length $10$ is the longest. Check if it's mentioned, or if it's the leg opposite the right angle.

EDIT: Noticing your question again, you actually said "the leg of a right angle"...so I guess you can disregard anything below the first paragraph.