Question

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Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta = 25^{\circ}\), the hypotenuse \(c = 9\), and the side opposite to the angle \(\theta\) is \(x\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the sine formula

We know that \(\sin\theta=\frac{x}{9}\), where \(\theta = 25^{\circ}\). So, \(x = 9\times\sin(25^{\circ})\).

Step3: Calculate the value of \(\sin(25^{\circ})\)

Using a calculator, \(\sin(25^{\circ})\approx0.4226\).

Step4: Find the value of \(x\)

\(x = 9\times0.4226=3.8034\approx3.8\)

Answer:

\(x\approx3.8\)