Question

find the length of side x to the nearest tenth.
(right triangle with angles 30°, 60°, right angle; hypotenuse √11, side x opposite 30°? wait, no, angles: 30°, 60°, right angle, so sides: hypotenuse, 30° opposite side, 60° opposite side. wait, the triangle has angles 30°, 60°, right angle, hypotenuse √11, and side x. need to find x. answer attempt 1 out of 2 x = blank submit ans

Explanation:

Step1: Identify trigonometric ratio

For the 30° angle, side $x$ is opposite, and $\sqrt{11}$ is the hypotenuse. Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(30^\circ) = \frac{x}{\sqrt{11}}$

Step3: Solve for $x$

$x = \sqrt{11} \times \sin(30^\circ)$
Since $\sin(30^\circ) = 0.5$, substitute:
$x = \sqrt{11} \times 0.5$
Calculate $\sqrt{11} \approx 3.3166$, so:
$x \approx 3.3166 \times 0.5 = 1.6583$

Step4: Round to nearest tenth

$x \approx 1.7$

Answer:

$x = 1.7$