Let's begin by color coding the opposite angles, sides, and the vertices in the given triangle. It will help us to use the Law of Sines later.
Let's first find the measure of the third interior angle which is m∠ G, and then the measures of the missing side lengths one at a time.
Finding m ∠ G
To find m ∠ G we can use the Triangle Angle Sum Theorem. This tells us that the measures of the angles in a triangle add up to 180.
m∠ G+ 34 + 71 = 180 ⇔ m ∠ G = 75
Finding GH
Note that we know the m ∠ G and the length of the side which is opposite to this angle. We want to find the length of the side j that is opposite to the ∠ J. Therefore, it is time to use the Law of Sines!
sin G/g =sin J/j
Let's substitute g= 20.3, m ∠ G= 75, and m ∠ J= 71 to isolate j.
