Question

Find the missing side length to the nearest tenth of a millimeter. Enter your answer in the box.

A right triangle with one leg 5 point 2 millimeters and hypotenuse 7 millimeters.

About
mm

Answer 1

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

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

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

In this case:
- one leg \(a = 5.2\) mm,
- hypotenuse \(c = 7\) mm,
- we need to find the other leg \(b\).

We can rearrange the Pythagorean theorem to solve for \(b\):

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

Now, substituting in the values:

\[
b^2 = 7^2 - 5.2^2
\]
\[
b^2 = 49 - 27.04
\]
\[
b^2 = 21.96
\]

Now, taking the square root to find \(b\):

\[
b = \sqrt{21.96} \approx 4.68
\]

Rounding to the nearest tenth of a millimeter, we obtain:

\[
b \approx 4.7 \text{ mm}
\]

Thus, the missing side length is approximately \(4.7\) mm.