Question

choose the correct values for x and y in the right triangle.
y = 3\sqrt{6}
y = 6\sqrt{3}
x = 6\sqrt{3}
x = 9

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, if the angle is $\theta = 60^{\circ}$ and the side adjacent to the $60^{\circ}$ angle is $a = 3\sqrt{3}$. We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Find $x$ using $\tan$ ratio

$\tan60^{\circ}=\sqrt{3}=\frac{x}{3\sqrt{3}}$. Cross - multiply gives $x = 3\sqrt{3}\times\sqrt{3}=9$.

Step3: Find $y$ using $\cos$ ratio

$\cos60^{\circ}=\frac{1}{2}=\frac{3\sqrt{3}}{y}$. Cross - multiply gives $y = 6\sqrt{3}$.

Answer:

$y = 6\sqrt{3}$, $x = 9$