Question

Consider the figure shown below. How long is HG?

Answer 1

HG = 2
`√(2)`

Explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° =
`(1)/(2)` , then

cos60° =
`(adjacent)/(hypotenuse)` =
`(GI)/(HG)` =
`(√(2) )/(HG)` =
`(1)/(2)` ( cross- multiply )

HG = 2
`√(2)`

Answer 2

Use trigonometry.

Angle H = 30 degrees

sin (30) = sqrt{2}/HG

HG = sqrt{2}/sin (30)

HG = 2.8284271248

HG = 2•sqrt{2}