Question

choose the correct values for x and y in the right triangle. y = 3√3 x = 6 y = 6 x = 3√3

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, if one of the non - right angles is $30^{\circ}$, and the side opposite the $30^{\circ}$ angle is $a$, the side opposite the $60^{\circ}$ angle is $a\sqrt{3}$, and the hypotenuse is $2a$. Assume the side of length $3$ is opposite the $30^{\circ}$ angle.

Step2: Find the value of $x$

The side $x$ is opposite the $60^{\circ}$ angle. Using the ratio, if the side opposite $30^{\circ}$ is $3$, then $x = 3\sqrt{3}$.

Step3: Find the value of $y$

The side $y$ is the hypotenuse. Since the side opposite $30^{\circ}$ is $3$, then $y=2\times3 = 6$.

Answer:

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