In triangle ghi, angle g = 109, angle i = 15, h = 5. find g to the nearest tenth.

4.4

5.7

18.3

1.4

You have to use the Law of Sines here, but in order to do that, you need to find the measure of angle H. That's easy cuz you have the measures of the other 2. Also, it's important to realize that this is NOT a right triangle, so Pythagorean's Theorem does not apply. Angle H = 180 - 109 - 15 which is 56 degrees. Now set up your ratios using the Law of Sines, side g, angle G, side h, and angle H:
g/sin(109) = 5/sin(56). Cross multiply to get g sin(56) = 5 sin(109). Divide both sides by sin(56) to get g = sin(109)/sin(56) and g = 5.7.