The Pythagorean Theorem is a²+b²=c², where "a" and "b" are side lengths of a right triangle, and c is the hypotenuse of the right triangle. We are given a side length of 30 inches and a hypotenuse of 34 inches, which will be "a" and "c" respectively. Therefore, we can solve for b, the missing side length:
a²+b²=c²
30²+b²=34²
900+b²=1156
b²=256
b=16
Therefore, the missing side length is 16 inches, making the area of the triangle A=bh=(30)(16)=480 in².
