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If JE = 4.8 and EW = 28.6, find the length of JW. Round your answer to the nearest tenth if necessary. You must show ALL work in order to receive full credit.

JE = 4.8 and EW = 28.6 are the legs JW is the hypotenuse
the triangle is a right triangle

5 answers

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:

\[ \boxed{29.0} \]

EW = 28.6 not 23.04

I apologize for any confusion; however, it appears that you are mixing up the values. Let me clarify and recalculate the solution step-by-step.

Given:

  • \( JE = 4.8 \)
  • \( EW = 28.6 \)

We need to find the length of the hypotenuse \( JW \) in the right triangle, where \( JE \) and \( EW \) represent the two legs.

Using the Pythagorean theorem: \[ c^2 = a^2 + b^2 \] where:

  • \( c = JW \)
  • \( a = JE = 4.8 \)
  • \( b = EW = 28.6 \)

Substituting in the values: \[ JW^2 = JE^2 + EW^2 \]

Calculating each part:

  1. Calculate \( JE^2 \): \[ JE^2 = (4.8)^2 = 23.04 \]

  2. Calculate \( EW^2 \): \[ EW^2 = (28.6)^2 = 816.96 \]

Now substitute back into the theorem: \[ JW^2 = 23.04 + 816.96 \]

Calculating this sum: \[ JW^2 = 840 \]

Now take the square root to find \( JW \): \[ JW = \sqrt{840} \]

Calculating the square root: \[ JW \approx 29.0 \]

So, rounding to the nearest tenth, the length of \( JW \) is: \[ \boxed{29.0} \]

Thank you for your patience, and if there are further clarifications needed, please let me know!

sorry

No problem at all! Mistakes happen, and I'm here to help. If you have any further questions or need assistance with anything else—math-related or otherwise—please feel free to ask!