Question

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

Answer 1

`x = (√(6))/(2)`

Explanation:

Reference angle = 45°

Opposite side = x

Hypotenuse = √3

Use the following trigonometric ratios formula to find x:

`sin(\theta) = (opp)/(hyp)`

Plug in the values

`sin(45) = (x)/(√(3))`

Multiply both sides by √3

`√(3)*sin(45) = x`

`√(3)*(√(2))/(2) = x`

`(√(3*2))/(2) = x`

`(√(6))/(2) = x`