To find the unknown side length in a right triangle using the Pythagorean Theorem, you can use the formula:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) and \( b \) are the lengths of the two legs of the triangle,
- \( c \) is the length of the hypotenuse.
In this case, you have a width (leg) of 3 and a slope (which is also a leg in a right triangle context) of 15. We can assume that the slope represents one leg adjacent to the width.
Let's label:
- \( a = 3 \) (the width),
- \( b = 15 \) (the slope).
Now we can use the Pythagorean Theorem to find the hypotenuse \( c \):
\[ c^2 = a^2 + b^2 \]
Substituting values:
\[ c^2 = 3^2 + 15^2 \] \[ c^2 = 9 + 225 \] \[ c^2 = 234 \]
Now, take the square root to find \( c \):
\[ c = \sqrt{234} \approx 15.3 \]
Therefore, the unknown side length (hypotenuse) rounded to the nearest tenth is approximately 15.3.