Question

What are the values of x and y?

Answer 1

Answer:

B)   x = 8$\sqrt{3}$ ;  y = 4$\sqrt{3}$

Step-by-step explanation:

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

1 : $\sqrt{3}$ : 2

we can find 'x' by creating this proportion:

12/$\sqrt{3}$ = x/2

cross-multiply to get:

$\sqrt{3}$x = 24

x = 24/$\sqrt{3}$

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

multiply numerator and denominator by $\sqrt{3}$ to get:

(24$\sqrt{3}$)÷3, which is 8$\sqrt{3}$

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

therefore y = 4$\sqrt{3}$