Question

Find the missing side length. Round your answer to the nearest tenth if necessary.

Right triangle with side length 5 cm and hypotenuse length 8 cm.

cm

Answer 1

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

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

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

In this case, we know:

- One side (\(a\)) = 5 cm
- Hypotenuse (\(c\)) = 8 cm

We need to find the length of the other side (\(b\)). Plugging in the known values:

\[
5^2 + b^2 = 8^2
\]

Calculating the squares:

\[
25 + b^2 = 64
\]

Next, we isolate \(b^2\) by subtracting 25 from both sides:

\[
b^2 = 64 - 25
\]
\[
b^2 = 39
\]

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

\[
b = \sqrt{39}
\]

Calculating the square root:

\[
b \approx 6.244
\]

Rounding to the nearest tenth gives us:

\[
b \approx 6.2
\]

Therefore, the missing side length is approximately **6.2 cm**.