Consider the figure shown below. How long is HG?

Answer:
HG = 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{GI}{HG}[/tex] = [tex]\frac{\sqrt{2} }{HG}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
HG = 2[tex]\sqrt{2}[/tex]
Use trigonometry.
Angle H = 30 degrees
sin (30) = sqrt{2}/HG
HG = sqrt{2}/sin (30)
HG = 2.8284271248
HG = 2•sqrt{2}