In triangle HIJ, given h= 6 units, i = 10 units and I= 30 deg, Calculate angle H.

To find angle H 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 the angle opposite that side is the same for all three sides of the triangle.

Here's how you can apply it:

1. First, we know that angle I is 30 degrees and the side opposite to it (i) is 10 units. So, we can write the ratio for angle I as follows: sin(I)/i = sin(30)/10.

2. We also know that side h is 6 units, and we want to find the angle opposite to it, which is angle H. So, we can write the ratio for angle H as follows: sin(H)/h = sin(H)/6.

3. According to the Law of Sines, these two ratios should be equal. So, we have the equation: sin(30)/10 = sin(H)/6.

4. To solve for sin(H), we can cross-multiply and get: sin(H) = (6 * sin(30))/10.

5. Calculate the value of sin(30), which is 0.5, and substitute it into the equation: sin(H) = (6 * 0.5)/10 = 3/10 = 0.3.

6. To find the angle H, we need to find the inverse sine (also known as arcsin) of 0.3.

7. Using a calculator, arcsin(0.3) is approximately 17.46 degrees.

So, angle H in triangle HIJ is approximately 17.46 degrees.