Question

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

Answer 1

x =
`(8√(3) )/(3)`

Explanation:

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

sin60° =
`(√(3) )/(2)`

sin60° =
`(opposite)/(hypotenuse)` =
`(4)/(x)` =
`(√(3) )/(2)` ( cross- multiply )

x ×
`√(3)` = 8 ( divide both sides by
`√(3)` )

x =
`(8)/(√(3) )` ×
`(√(3) )/(√(3) )` ( rationalising the denominator )

x =
`(8√(3) )/(3)`