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, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the lengths of the sides are:
- One leg: 8 in
- Hypotenuse: 12 in
- Other leg: y
So the equation we would use to find the length of the other leg (y) is:
8^2 + y^2 = 12^2
Simplifying:
64 + y^2 = 144
Subtracting 64 from both sides:
y^2 = 80
Taking the square root of both sides:
y = √80
Therefore, the length of the other leg, y, is equal to √80 in, or approximately 8.94 in.