The wide-flange beam acts as a cantilever. Due to an error it is installed at an angle \(\theta\) with the vertical. Determine the ratio of its displacement in the \(x\) direction to its displacement in the \(y\) direction at \(A\) when a load \(\mathbf{P}\) is applied at this point. The moments of inertia are \(I_{x}\) and \(I_{y}\). For the solution, resolve \(\mathbf{P}\) into components and use the method of superposition. The result indicates that large lateral deflections ( \(x\) direction) can occur in narrow beams, \(I_{y} \ll I_{x}\), when they are improperly installed in this manner. To show this numerically, calculate the deflections in the \(x\) and \(y\) directions for an A-36 steel W10 \(\times 15\), with \(P=1.5 \mathrm{kip}, \theta=10^{\circ}\), and \(L=12 \mathrm{ft}\).