I just need the length of the unknown side and why it makes sense

Answer:
Step-by-step explanation:
According to Pythagorean theorem, the square value of hypotenuse (the side length that sees angle measure 90) is equal to sum of square value of two legs:
let x represent the missing length
x^2 + 3^2 = 7^2
x^2 + 9 = 49 subtract 9 from both sides
x^2 = 40 find the root for both sides
x = [tex]\sqrt{40}[/tex] or 6.3 inches approximately