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# Find the length of GI in the triangle below. (Geometry Question)?

Can someone give a detailed explanation on how to find this answer? I'm having a lot of trouble with it, thank you!

### 2 Answers

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- TomVLv 71 month agoFavorite Answer
Use the Law of Cosines:

c² = a² + b² - 2ab cosC

where c is the side of the triangle opposite angle C

In the given triangle, let

a = GH =60

b = HI = 42

c = GI

C = 123°

c² = 60² + 42² - 2(60)(42) cos123° = 8108.9807...

c ≈ 90.050

- SlowfingerLv 61 month ago
Cosine Law

GI² = GH² + HI² - 2 GH HI cos ∠H

GI = √(GH² + HI² - 2 GH HI cos ∠H)

GI = √(60² + 42² - 2*60*42*cos 123°)

GI = 90.05

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