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

a =
inches

b = 17, c = 15

1 answer

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.