Question

Find the missing lengths. Round to the nearest tenth.

The hypotenuse of the right triangle is twenty one while the shorter leg is four. What's the longer leg?

Answer 1

To find the length of the longer leg of a right triangle when the hypotenuse and the shorter leg are known, we can use the Pythagorean theorem:

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

where:
- \( a \) is one leg (the shorter leg),
- \( b \) is the other leg (the longer leg),
- \( c \) is the hypotenuse.

In this case:
- \( a = 4 \) (the shorter leg),
- \( c = 21 \) (the hypotenuse).

We are solving for \( b \). Plugging the values into the theorem gives us:

\[
4^2 + b^2 = 21^2
\]

Calculating the squares:

\[
16 + b^2 = 441
\]

Now, subtract 16 from both sides:

\[
b^2 = 441 - 16
\]
\[
b^2 = 425
\]

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

\[
b = \sqrt{425}
\]

Calculating \( \sqrt{425} \):

\[
b \approx 20.6
\]

Rounding to the nearest tenth, the length of the longer leg is approximately **20.6**.