Question

3 multiple choice 1 point find the value of the variable(s). if your answer is not an integer, leave it in simplest radical form. not drawn to scale

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Given \(\theta = 30^{\circ}\) and the opposite side to \(30^{\circ}\) is \(17\), and the hypotenuse is \(y\).
Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\sin30^{\circ}=\frac{17}{y}\).

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Step2: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 30^{\circ}\), opposite side \(= 17\) and adjacent side \(=x\).
Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(\tan30^{\circ}=\frac{17}{x}\).

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Answer:

\(x = 17\sqrt{3},y = 34\) (First option)