Question

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

Answer 1

x = 2

Explanation:

We can use the sine or cosine ratio to solve for x

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

cos45° =
`(√(2) )/(2)`, then

cos45° =
`(adjacent)/(hypotenuse)` =
`(x)/(√(8) )` =
`(√(2) )/(2)` ( cross- multiply )

2x =
`√(8)` ×
`√(2)` =
`√(16)` = 4 ( divide both sides by 2 )

x = 2