Question

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

Answer 1

x = 2
`√(3)`

Explanation:

Using the tangent ratio in the right triangle with either of the 2 angles and the exact value

tan60° =
`√(3)`

tan60° =
`(opposite)/(adjacent)` =
`(6)/(x)` =
`√(3)`

Multiply both sides by x

6 = x
`√(3)` ( divide both sides by
`√(3)` )

x =
`(6)/(√(3) )` ×
`(√(3) )/(√(3) )` ← rationalising the denominator

x =
`(6√(3) )/(3)` = 2
`√(3)`