Since x is the side adjacent the \(77^{\circ}\) angle and we are given the length of the side opposite the angle, then we can use the tangent ratio to write

\(\tan=\frac{\text{opposite leg}}{\text{adjacent leg}}\)

\(\tan77^{\circ}=\frac{130}{x}\)

\(x=\frac{130}{\tan77^{\circ}}\)

\(x\approx30m\)