Question

solve for x. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary.
draw
show your work here
hint: to add the square root symbol (√□), type
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Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the opposite side to the \(30^{\circ}\) angle is \(x\), and the hypotenuse is \(18\). So, \(\sin30^{\circ}=\frac{x}{18}\).

Step2: Substitute the value of \(\sin30^{\circ}\)

We know that \(\sin30^{\circ}=\frac{1}{2}\). Then \(\frac{1}{2}=\frac{x}{18}\).

Step3: Solve for \(x\)

Cross - multiply: \(x=\frac{1\times18}{2}=9\).

Answer:

\(x = 9\)