what is the the missing leg

hypotenuse 20cm a leg is 12cm

1 answer

To find the missing leg of a right triangle when you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem, which states:

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

where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.

In your case:

  • \(c = 20, \text{cm}\) (hypotenuse)
  • \(a = 12, \text{cm}\) (one leg)
  • \(b\) is the missing leg.

Plugging in the values, we get:

\[ 12^2 + b^2 = 20^2 \]

Calculating the squares:

\[ 144 + b^2 = 400 \]

Now, subtract 144 from both sides:

\[ b^2 = 400 - 144 \] \[ b^2 = 256 \]

Now, take the square root of both sides to find \(b\):

\[ b = \sqrt{256} \] \[ b = 16, \text{cm} \]

So, the missing leg is 16 cm.