Question

find the length of side $x$ to the nearest tenth.
(there is a right triangle with one leg labeled 11, one angle 30°, one angle 60°, and hypotenuse labeled $x$)
answer attempt 1 out of 2
$x = \square$

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For the $30^\circ$ angle, the opposite side is the side adjacent to the $60^\circ$ angle, and the hypotenuse is $x$. First, find the side opposite the $30^\circ$ angle relative to $x$: the side with length 11 is opposite the $60^\circ$ angle, so for the $30^\circ$ angle, $\sin(30^\circ) = \frac{\text{side adjacent to }60^\circ}{x}$, but alternatively, use $\sin(60^\circ) = \frac{11}{x}$.

Step2: Rearrange to solve for $x$

Rearrange the formula to isolate $x$: $x = \frac{11}{\sin(60^\circ)}$

Step3: Calculate the value

$\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660$, so $x \approx \frac{11}{0.8660} \approx 12.7$

Answer:

$x \approx 12.7$