Question

for the triangle shown, what are the values of $x$ and $y$?
select the correct answer.
$\bigcirc$ $x = 2\sqrt{3}, y = 4\sqrt{3}$
$\bigcirc$ $x = 3\sqrt{3}, y = 6\sqrt{3}$
$\bigcirc$ $x = 6\sqrt{3}, y = 12$
$\bigcirc$ $x = 6\sqrt{3}, y = 12\sqrt{3}$

Explanation:

Step1: Find x using tangent

$\tan(30^\circ) = \frac{x}{6}$
$x = 6 \times \tan(30^\circ) = 6 \times \frac{\sqrt{3}}{3} = 2\sqrt{3}$

Step2: Find y using cosine

$\cos(30^\circ) = \frac{6}{y}$
$y = \frac{6}{\cos(30^\circ)} = \frac{6}{\frac{\sqrt{3}}{2}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}$

Answer:

$x = 2\sqrt{3}, y = 4\sqrt{3}$