If you have a right triangle with one leg side 8 in, the hypotenuse is 12 in, and the other leg is unknown, y.
What is the equation you would use to find the length of side y ?
To find the length of the other leg (side y) in a right triangle, you can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this can be expressed as:
a^2 + b^2 = c^2
In this case, if one leg is 8 inches (let's call this "a"), the hypotenuse is 12 inches (let's call this "c"), and the other leg is unknown (let's call this "y" or "b"), the equation would be:
8^2 + y^2 = 12^2
64 + y^2 = 144
Now, solving for y:
y^2 = 144 - 64
y^2 = 80
Taking the square root of both sides to solve for y:
y = √80
y ≈ 8.94 inches
Therefore, the length of the unknown leg (side y) in this right triangle is approximately 8.94 inches.