A right triangle has one eg of length (y) and the hypotenuse of length (x). what is the length of the other leg of this triangle

1 answer

In a right triangle, you can use the Pythagorean theorem to find the length of the other leg. The theorem states that:

\[ a^2 + b^2 = c^2 \]

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.

In your case, let’s denote:

  • the length of one leg as \(y\),
  • the length of the hypotenuse as \(x\),
  • the length of the other leg as \(z\).

According to the Pythagorean theorem:

\[ y^2 + z^2 = x^2 \]

To find the length of the other leg \(z\), rearrange the equation:

\[ z^2 = x^2 - y^2 \]

Now, take the square root of both sides to solve for \(z\):

\[ z = \sqrt{x^2 - y^2} \]

So, the length of the other leg is:

\[ z = \sqrt{x^2 - y^2} \]

Make sure that \(x\) is greater than \(y\) for the lengths to be valid in a right triangle.