To apply the Pythagorean theorem, we use the formula:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides of the triangle.
In this triangle, you mentioned that the width (let's assume this is one side) is 3, and the slope (which we can assume is the other side) is 15. Hence:
- \(a = 3\)
- \(b = 15\)
Now we’ll plug these values into the Pythagorean theorem:
\[ 3^2 + 15^2 = c^2 \]
Calculating each term:
\[ 3^2 = 9 \] \[ 15^2 = 225 \] \[ 9 + 225 = c^2 \] \[ 234 = c^2 \]
Now take the square root to find \(c\):
\[ c = \sqrt{234} \approx 15.3 \]
Rounding to the nearest tenth, we find that the length of the hypotenuse is approximately:
15.3.
Therefore, the answer is: 15.3