SOLUTION: In Triangle GHI, h=8, i=12 and M∠G = 96 degrees. Find M∠I to the nearest tenth. Thanks!

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Question 1015730: In Triangle GHI, h=8, i=12 and M∠G = 96 degrees. Find M∠I to the nearest tenth.
Thanks!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the law of cosines,
g%5E2=h%5E2%2Bi%5E2-2hicos%28G%29
g%5E2=8%5E2%2B12%5E2-2%288%29%2812%29cos%2896%29
g%5E2=64%2B144-192%28-.1045%29
g%5E2=228.07
g=15.1
So then using the law of cosines again,
i%5E2=g%5E2%2Bh%5E2-2ghcos%28I%29
cos%28I%29=%28i%5E2-g%5E2-h%5E2%29%2F%28-2gh%29
cos%28I%29=%28144-228.07-64%29%2F%28-2%2815.1%29%288%29%29
cos%28I%29=0.6129
I=52.2