Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.  JK=𝐽𝐾=  ;  JL=𝐽𝐿=  ;  m∠K𝑚∠𝐾  °

To solve a right triangle given two sides $JK$ and $JL$ along with one angle $m\angle K$, we can follow these steps:

1. Break Down the Problem

   We are given:

   • Side $JK$ (one leg of the triangle).
   • Side $JL$ (the other leg of the triangle).
   • Angle $m\angle K$ (one of the angles in the triangle).

   We need to compute the following:

   • The length of the hypotenuse $KL$.
   • The remaining angle $m\angle J$.

2. Relevant Concepts

   • Pythagorean Theorem: For a right triangle, the relation is given by: $c^2 = a^2 + b^2$ Where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides.
   • Angle Sum in a Triangle: The sum of angles in a triangle is 180°. Thus, $m\angle J + m\angle K + 90° = 180°$ Therefore: $m\angle J = 90° - m\angle K$

3. Analysis and Detail

   • Assuming the lengths of the sides are as follows:
     • $JK = a$
     • $JL = b$
   • Using the Pythagorean theorem to find $KL$: $KL = \sqrt{JK^2 + JL^2} = \sqrt{a^2 + b^2}$
   • To find the angle $m\angle J$: $m\angle J = 90° - m\angle K$

4. Verify and Summarize

   • Calculate $KL$ and confirm that the calculated values of angles and sides satisfy the conditions of a right triangle.
   • Summarize the measures of the sides and angles rounded as requested.

Final Answer

The measures of the triangle are as follows:

• Side $KL$ (hypotenuse) rounded to the nearest tenth.
• Angle $m\angle J$ rounded to the nearest degree.

Please provide the specific values for $JK$, $JL$, and $m\angle K$ so I can substitute and calculate the exact numbers for $KL$ and $m\angle J$.