Question

find the value of x.
$x = \square$ yd. (round to the nearest tenth as needed.)

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the hypotenuse = 490 yd, the angle = 19°, and $x$ is the side opposite the given angle. We use the sine function: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(19^\circ)=\frac{x}{490}$

Step3: Solve for x

Rearrange to isolate $x$: $x = 490 \times \sin(19^\circ)$
Calculate $\sin(19^\circ)\approx0.3256$, so $x\approx490\times0.3256$

Step4: Compute final value

$490\times0.3256=159.544$
Round to the nearest tenth: $x\approx159.5$

Answer:

159.5 yd