To find the missing side in the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle:
Side a = 5
Side b = 3
Side c = 12 (the hypotenuse)
Side y = unknown
Using the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values:
5^2 + 3^2 = 12^2
25 + 9 = 144
34 ≠ 144
Since the equation is not balanced, we made an error while labeling the sides. Let's relabel them correctly:
Side a = 3
Side b = y (unknown)
Side c = 5
Side y = 9
Using the Pythagorean theorem again:
a^2 + b^2 = c^2
Substituting the new values:
3^2 + y^2 = 5^2
9 + y^2 = 25
y^2 = 25 - 9
y^2 = 16
y = √16
y = 4
Therefore, the missing side y in the triangle is 4.