Question

what is the the missing leg

hypotenuse 20cm a leg is 12cm

Answer 1

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**.