Find the length of GI in the triangle below. Please explain how you got the answer if possible because I'm super confused, thanks!!

90

Step-by-step explanation:

From the question given above, the following data were obtained:

Length GH = i = 60

Lenght HI = g = 42

Angle H = 123°

Length (GI) = h =?

Thus the length GI (i.e h) can be obtained by using the cosine rule formula as shown below:

h² = i² + g² – 2ig Cos H

h² = 60² + 42² – 2 × 60 × 42 × Cos 123

h² = 3600 + 1764 – (5040 × –0.5446)

h² = 5364 – (–2744.784)

h² = 5364 + 2744.784

h² = 8108.784

Take the square root of both side

h = √8108.784

h = 90

Thus, the Lenght of GI is 90