Question

12 ft width 13 ft slope
What is the length of the missing leg? If necessary, round to the nearest tenth.
a = _ feet

Answer 1

To find the length of the missing leg in a right triangle where one leg (width) is 12 feet and the other leg (the height defined by the slope) is 13 feet, we can use the Pythagorean theorem. The theorem is stated as:

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

Where:
- \(a\) is one leg
- \(b\) is the other leg
- \(c\) is the hypotenuse (the slope in this case)

In this instance, if we define:
- \(a = 12\) ft (width)
- \(c = 13\) ft (slope)

We need to find \(b\), the missing leg (height):

\[
12^2 + b^2 = 13^2
\]

Calculating the squares:

\[
144 + b^2 = 169
\]

Now, isolate \(b^2\):

\[
b^2 = 169 - 144
\]
\[
b^2 = 25
\]

Now, take the square root of both sides to find \(b\):

\[
b = \sqrt{25} = 5
\]

Thus, the length of the missing leg \(b\) is **5 feet**.

So rounding to the nearest tenth, the answer remains **5.0 feet**.