Answer:
To find the length of the other leg, b, in a right triangle with a hypotenuse length of c=13 and one leg length of a=5, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
So, we have:
a^2 + b^2 = c^2
Substituting the given values, we get:
5^2 + b^2 = 13^2
25 + b^2 = 169
Now, let's solve for b:
b^2 = 169 - 25
b^2 = 144
Taking the square root of both sides, we find:
b = 12
Therefore, the length of the other leg, b, is 12 units.