Question

What is the length of the missing leg? If necessary, round to the nearest ten
a =
inches

b = 17, c = 15

Answer 1

To find the length of the missing leg (a) in a right triangle, you can use the Pythagorean theorem, which states that:

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

Where:
- \( a \) is the length of the missing leg,
- \( b \) is the length of one leg (17 inches),
- \( c \) is the length of the hypotenuse (15 inches).

However, it appears there might be a misunderstanding because in a right triangle, the hypotenuse is always the longest side. Here, \( c = 15 \) is less than \( b = 17 \). If 17 is one leg, then 15 cannot be the hypotenuse.

If you meant for \( b \) to be the hypotenuse, you can calculate \( a \) as follows:

\[
a^2 + 15^2 = 17^2
\]

Calculating the squares:

\[
a^2 + 225 = 289
\]

Now, isolate \( a^2 \):

\[
a^2 = 289 - 225
\]
\[
a^2 = 64
\]

Now take the square root:

\[
a = \sqrt{64} = 8
\]

So, the length of the missing leg \( a \) is **8 inches**.

Since the problem asks to round to the nearest ten, you would round 8 inches to **10** inches.