Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

x = 2
`√(2)`

Explanation:

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

cos45° =
`(√(2) )/(2)` , then

cos45° =
`(adjacent)/(hypotenuse)` =
`(x)/(4)` =
`(√(2) )/(2)` ( cross- multiply )

2x = 4
`√(2)` ( divide both sides by 2 )

x = 2
`√(2)`