Question

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

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the adjacent side is \(x\), and the hypotenuse is \(20\). So, \(\cos30^{\circ}=\frac{x}{20}\).

Step2: Substitute the value of \(\cos30^{\circ}\)

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\). Then \(\frac{\sqrt{3}}{2}=\frac{x}{20}\).

Step3: Solve for \(x\)

Cross - multiply: \(x = 20\times\frac{\sqrt{3}}{2}\). Simplify the expression: \(x = 10\sqrt{3}\).

Answer:

\(x = 10\sqrt{3}\)