Question

9 yd width 15 yd slope
What is the length of the missing leg? If necessary, round to the nearest tenth.
a = _ yards

Answer 1

To find the length of the missing leg of a right triangle, you will typically use the Pythagorean theorem, which states:

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

where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg (in your case the width), and
- \( c \) is the hypotenuse (in your case the slope).

In your scenario:
- \( b = 9 \) yards (width)
- \( c = 15 \) yards (slope)

We need to find \( a \):

\[
a^2 + 9^2 = 15^2
\]

Calculating \( 9^2 \) and \( 15^2 \):

\[
a^2 + 81 = 225
\]

Now, subtract 81 from both sides:

\[
a^2 = 225 - 81
\]
\[
a^2 = 144
\]

Now, take the square root of both sides:

\[
a = \sqrt{144} = 12
\]

Thus, the length of the missing leg \( a \) is:

\[
\boxed{12} \text{ yards}
\]