Question

use a trigonometric ratio to solve for x. round to two decimal places as necessary. draw show your work here x = use a trigonometric ratio to solve for x. round to two decimal places as necessary draw

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Here, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, and $\theta = 61^{\circ}$, the hypotenuse is 13 and the opposite side to the angle $61^{\circ}$ is $x$. So, $\sin61^{\circ}=\frac{x}{13}$.

Step2: Solve for $x$

We know that $\sin61^{\circ}\approx0.8746$. Then, $x = 13\times\sin61^{\circ}$. Substitute the value of $\sin61^{\circ}$ into the equation: $x=13\times0.8746 = 11.3698$.

Step3: Round the result

Rounding $11.3698$ to two decimal places, we get $x\approx11.37$.

Answer:

$11.37$