Question

The hypotenuse of a right triangle is 15 inches, and one of its legs is 11 inches. What is the length of the other leg?

Answer 1

The missing leg, `b`, is `b = sqrt(104)`.

Explanation:

The Pythagorean Theorem is `a^2 = b^2 = c^2`. The `a` and `b` are each leg and the `c` is the hypotenuse. We can plug in our given information and solve like an equation to
find the missing variable.

Since we know `c`, the hypotenuse, is 15, we can put that in our equation. We also know that `a`, one of our legs, is 11, so we can put that into our equation as well. `11^2 + b^2 = 15^2`. This simplifies to `121 + b^2 = 225`. Simplified one more step, we get `b^2 = 104`.

To reverse the exponent, we must do the square root of each side. `sqrt(b^2) = sqrt(104)`. Since `sqrt(104)` is not rational, we will leave it in this form.

The missing leg, `b`, is `b = sqrt(104)`.