Question

What are the values of x and y?

Question 18 options:


A)


x = 8; y = 4


B)


x = 8
`√(3)` ; y = 4
`√(3)`


C)


x = 6
`√(x3)` ; y = 3
`√(3)`


D)


x = 4
`√(3)` ; y = 8
`√(3)`

Answer 1

B) x = 8
`√(3)` ; y = 4
`√(3)`

Explanation:

in a 30-60-90° triangle the sides, respectively, are in the ratio of

1 :
`√(3)` : 2

we can find 'x' by creating this proportion:

12/
`√(3)` = x/2

cross-multiply to get:

`√(3)`x = 24

x = 24/
`√(3)`

we can simplify this by 'rationalizing the denominator' which is to

multiply numerator and denominator by
`√(3)` to get:

(24
`√(3)`)÷3, which is 8
`√(3)`

we know that side 'y' is half that of side 'x'

therefore y = 4
`√(3)`