To find the length of \( JW \), which is the hypotenuse of the right triangle with legs \( JE \) and \( EW \), we can apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the legs.
In our case:
- \( a = JE = 4.8 \)
- \( b = EW = 28.6 \)
- We want to find \( JW \) (which is \( c \)).
Now, substituting the values into the formula:
\[ JW^2 = JE^2 + EW^2 \]
Calculating \( JE^2 \):
\[ JE^2 = (4.8)^2 = 23.04 \]
Calculating \( EW^2 \):
\[ EW^2 = (28.6)^2 = 816.96 \]
Now we can substitute these values back into the Pythagorean theorem:
\[ JW^2 = 23.04 + 816.96 = 840 \]
To find \( JW \), we take the square root of both sides:
\[ JW = \sqrt{840} \]
Now we will calculate \( \sqrt{840} \):
\[ JW \approx 29.0 \]
Finally, rounding to the nearest tenth, we find that the length of \( JW \) is:
\[ \boxed{29.0} \]