Question

find the value of x. round to the nearest tenth.
3
23
21
x
screenshot 2025 - 09 - 22 144811.png

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta = 23^{\circ}\), the hypotenuse \(c = 21\), and the side opposite to the angle \(\theta\) is \(x\). We use the sine ratio: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the formula

Substitute \(\theta = 23^{\circ}\) and \(c = 21\) into \(\sin\theta=\frac{x}{21}\). So, \(x = 21\times\sin(23^{\circ})\).

Step3: Calculate the value

We know that \(\sin(23^{\circ})\approx0.3907\). Then \(x = 21\times0.3907=8.2047\).

Answer:

\(8.2\)