Question

Using the 60-30-90 right triangle method, find x and answer in simplest radical form.

Answer 1

x = 2
`√(10)`

Explanation:

Since the triangle is right we can use the sine ratio to find x

sin60° =
`(opposite)/(hypotenuse)` =
`(√(30) )/(x)`

[ note the exact value of sin60° =
`(√(3) )/(2)` ], hence

`(√(3) )/(2)` =
`(30)/(x)`

multiply both sides by 2x, hence

`√(3)` x = 2
`√(30)`

divide both sides by
`√(3)`

x =
`(2√(30) )/(√(3) )` = 2
`\sqrt{(30)/(3) }` = 2
`√(10)`