Question

solve for w. do not convert your answer to decimal form. draw (triangle with right angle, base 15, angle 60° at base, height w)

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with one angle of \(60^{\circ}\), the adjacent side to the \(60^{\circ}\) angle is \(15\) and the opposite side is \(w\). The tangent function is defined as \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 60^{\circ}\), opposite \(=w\) and adjacent \( = 15\). So \(\tan(60^{\circ})=\frac{w}{15}\).

Step2: Solve for \(w\)

We know that \(\tan(60^{\circ})=\sqrt{3}\). Substituting this value into the equation \(\tan(60^{\circ})=\frac{w}{15}\), we get \(\sqrt{3}=\frac{w}{15}\). To solve for \(w\), we multiply both sides of the equation by \(15\): \(w = 15\times\sqrt{3}\).

Answer:

\(15\sqrt{3}\)