Question

what is the length of the missing leg if necessary round to the nearest tenth 10yd and 8yd what does b =

Answer 1

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

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

where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two legs. In your case, you have:

- One leg \(a = 8\, \text{yd}\)
- The other leg \(b = 10\, \text{yd}\) (which will be the hypotenuse)

We'll rearrange the formula to solve for the missing leg (one of the legs, which we'll denote as \(a\)) when \(c\) is the hypotenuse:

Using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]

If \(c = 10\, \text{yd}\) and \(b = 8\, \text{yd}\), then:
\[
a^2 + 8^2 = 10^2
\]
\[
a^2 + 64 = 100
\]
\[
a^2 = 100 - 64
\]
\[
a^2 = 36
\]
\[
a = \sqrt{36}
\]
\[
a = 6\, \text{yd}
\]

So the length of the missing leg is \(6\, \text{yd}\).