For context, there's a right triangle with top point J, bottom right point W, and bottom left point E. EW is the leg on the bottom of the triangle, JW is the hypotenuse, and JE is the other Leg

If JE=4.8 and EW=28.6, find the length of JW. Round your answer to the nearest tenth if necessary.
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1 answer

We can use the Pythagorean theorem to find the length of the hypotenuse \( JW \) in the right triangle. The Pythagorean theorem states:

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

where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse. In this case:

  • \( JE = 4.8 \) (one leg)
  • \( EW = 28.6 \) (the other leg)
  • \( JW \) is the hypotenuse which we want to find.

Substituting the known values into the Pythagorean theorem:

\[ (4.8)^2 + (28.6)^2 = JW^2 \]

Calculating \( (4.8)^2 \):

\[ (4.8)^2 = 23.04 \]

Calculating \( (28.6)^2 \):

\[ (28.6)^2 = 817.96 \]

Now, substituting these values back into the equation:

\[ 23.04 + 817.96 = JW^2 \]

Adding the two results:

\[ 841 = JW^2 \]

To find \( JW \), take the square root of both sides:

\[ JW = \sqrt{841} \]

Calculating the square root:

\[ JW = 29 \]

Thus, the length of the hypotenuse \( JW \) rounded to the nearest tenth is:

\[ \boxed{29.0} \]