Question

What is length of the missing leg of a right triangle with one leg 5 inches and the hypotenuse 8 inches? Make sure to do the calculations on a piece of paper.

39 inches

A sqrt(39) inches

B 9 inches

C sqrt(3) inches

D 3 inches

Answer 1

To find the length of the missing leg 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, we know one leg \( a = 5 \) inches and the hypotenuse \( c = 8 \) inches. We need to find the length of the other leg \( b \).

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

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

Substituting the known values:

\[
b^2 = 8^2 - 5^2
\]
\[
b^2 = 64 - 25
\]
\[
b^2 = 39
\]

Now, taking the square root of both sides to find \( b \):
\[
b = \sqrt{39}
\]

Therefore, the length of the missing leg of the triangle is \( \sqrt{39} \) inches.

Among the choices given, the correct answer is:

**A \( \sqrt{39} \) inches**.