Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the hypotenuse \(c = 620\) yd and the angle \(\theta=41^{\circ}\), and we want to find the side \(x\) (opposite side to the angle \(41^{\circ}\)). So we use the sine formula: \(\sin\theta=\frac{x}{c}\).

Step2: Substitute the values

Substitute \(\theta = 41^{\circ}\) and \(c = 620\) into the formula \(\sin\theta=\frac{x}{c}\). We get \(x = c\times\sin\theta\). Since \(\sin(41^{\circ})\approx0.6561\), then \(x=620\times\sin(41^{\circ})\).

Step3: Calculate the value

\(x = 620\times0.6561=406.782\approx406.8\) (rounded to the nearest tenth).

Answer:

\(406.8\)