Answer: HI = 5.3 cm
Let HI = x
GH = 2cm
m< H = 68 degrees
to find HI, we will need to apply the SOH CAH TOA RULE
HI = hypotenus
GH = adjacent
Cos 68 = adjacent / hypotenus
Cos 68 = 2 / x
Cross multiply
2 = x * cos 68
cos 68 = 0.3746
2 = x * 0.3746
Isolate x
x = 2/0.3746
x = 5.3cm
Therefore, HI is 5.3cm