Question

solve for w. do not convert your answer to decimal form. rationalize the denominator and simplify your answer if necessary.

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), the opposite side is \(w\) and the adjacent side is \(12\). So, \(\tan60^{\circ}=\frac{w}{12}\).

Step2: Substitute the value of \(\tan60^{\circ}\)

We know that \(\tan60^{\circ}=\sqrt{3}\). Then the equation becomes \(\sqrt{3}=\frac{w}{12}\).

Step3: Solve for \(w\)

Multiply both sides of the equation by \(12\): \(w = 12\sqrt{3}\).

Answer:

\(w = 12\sqrt{3}\)