Final answer:
The length of the third side (hypotenuse) of the right triangle is 13in.
Step-by-step explanation:
A right triangle has one angle measuring 90 degrees. The sides of a right triangle are called the legs and the hypotenuse. According to the Pythagorean Theorem, which applies to right triangles, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
Given that the two sides of the right triangle measure 5in and 12in, we can use the Pythagorean Theorem to find the length of the hypotenuse. Plugging in the values we have:
a² + b² = c² (where a and b are the lengths of the legs and c is the length of the hypotenuse)
5² + 12² = c²
25 + 144 = c²
169 = c²
c = √169
c = 13in
Therefore, the length of the third side (hypotenuse) of the right triangle is 13in.