Final answer:
To find the length of side j in triangle IJK, we can use the law of sines. Using the given values, the length of j is approximately 644.3 inches.
Step-by-step explanation:
To find the length of side j in triangle IJK, we can use the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles.
Using this formula, we can write:
j / sin(86°) = k / sin(29°)
Substituting the given values, we get:
j / sin(86°) = 590 / sin(29°)
Solving for j, we have:
j = (590 * sin(86°)) / sin(29°)
Calculating the value, j is approximately 644.3 inches to the nearest 10th of an inch.