Question

find v. 18√2 m 30° 60° write your answer in simplest radical form. meters

Explanation:

Step1: Use the sine rule

The sine rule states that in a triangle \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let the side opposite \(30^{\circ}\) be \(x\), opposite \(60^{\circ}\) be \(y\), and opposite \(90^{\circ}\) be \(18\sqrt{2}\). So \(\frac{v}{\sin60^{\circ}}=\frac{18\sqrt{2}}{\sin90^{\circ}}\).

Step2: Solve for \(v\)

Since \(\sin90^{\circ} = 1\) and \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), we have \(v = 18\sqrt{2}\times\frac{\sqrt{3}}{2}\). Simplifying gives \(v = 9\sqrt{6}\).

Answer:

\(9\sqrt{6}\) meters