In ΔHIJ, i = 2.8 inches, mm∠I=68° and mm∠J=50°. Find the length of j, to the nearest 10th of an inch.

To find the length of side j in triangle HIJ, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle.

Here's how you can apply it:

1. First, find the measure of angle H. Since the sum of the angles in a triangle is 180°, you can subtract the given angles from 180° to find angle H.

   So, m∠H = 180° - 68° - 50° = 62°

2. Now, you can set up the ratio of the sides to the sines of their opposite angles. According to the Law of Sines,

   i/sin(I) = j/sin(J)

   Substitute the given values into the equation:

   2.8/sin(68°) = j/sin(50°)

3. Solve the equation for j:

   j = (2.8/sin(68°)) * sin(50°)

4. Calculate the value:

   j ≈ 2.3 inches

So, the length of side j is approximately 2.3 inches.