Question

1. find the value of x.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), we know the side \(AB = 12\) (opposite side to the angle \(35^{\circ}\)) and we need to find the hypotenuse \(AC=x\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin35^{\circ}=\frac{AB}{AC}\).

Step2: Substitute the values and solve for \(x\)

Since \(\sin35^{\circ}\approx0.5736\) and \(AB = 12\), from \(\sin35^{\circ}=\frac{12}{x}\), we can rewrite the equation as \(x=\frac{12}{\sin35^{\circ}}\).
Substitute \(\sin35^{\circ}\approx0.5736\) into the equation: \(x=\frac{12}{0.5736}\approx20.9\).

Answer:

\(20.9\)