Find the sum of $u+v$, given that $|u|=45,|v|=34$, and $\theta=90^{\circ}$, where $\theta$ is the angle between $u$ and $v$. Give the magnitude to the nearest tenth and give the direction by specifying to the nearest degree the angle that the resultant makes with $\mathbf{u}$. The magnitude of $u+v$ is (Round to the nearest tenth.) The angle that $\mathbf{u}+\mathbf{v}$ makes with $\mathbf{u}$ is degrees. (Round to the nearest degree.)

Step 1 ：Given that |u|=45, |v|=34, and θ=90°, we can substitute these values into the formulas to find the magnitude and direction of the sum of the vectors.

Step 2 ：First, we calculate the magnitude of the sum of the vectors using the formula: \(|u+v| = \sqrt{|u|^2 + |v|^2 + 2|u||v|cos(\theta)}\). Substituting the given values, we get a magnitude of approximately 56.4 (rounded to the nearest tenth).

Step 3 ：Next, we calculate the direction of the sum of the vectors using the formula: \(\tan(\phi) = \frac{|v|sin(\theta)}{|u| + |v|cos(\theta)}\). Substituting the given values, we get a direction of approximately 37° (rounded to the nearest degree).

Step 4 ：Final Answer: The magnitude of $u+v$ is \(\boxed{56.4}\) and the angle that $\mathbf{u}+\mathbf{v}$ makes with $\mathbf{u}$ is \(\boxed{37^\circ}\).