Question

What is the length of the missing side of the triangle below? If needed, please round to the nearest tenth.

The longer leg is length 20


the hypotenuse is length 25'

What's the missing length?

Answer 1

To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states:

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

where:
- \( a \) and \( b \) are the lengths of the two legs of a right triangle,
- \( c \) is the length of the hypotenuse.

In this case, we have:
- The longer leg (\( b \)) is 20,
- The hypotenuse (\( c \)) is 25.

We need to find the length of the missing leg (\( a \)):

\[ a^2 + 20^2 = 25^2 \]

Calculating \( 20^2 \) and \( 25^2 \):

\[
20^2 = 400
\]

\[
25^2 = 625
\]

Now substitute these values into the equation:

\[
a^2 + 400 = 625
\]

Now, isolate \( a^2 \):

\[
a^2 = 625 - 400
\]

\[
a^2 = 225
\]

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

\[
a = \sqrt{225}
\]
\[
a = 15
\]

So, the length of the missing side is \( 15 \).