Answer
$41.8^{\circ}$
Work Step by Step
Step 1: We substitute vectors $\textbf {u}$ and $\textbf {v}$ in the formula for finding the angle between a pair of vectors, $\cos\theta=\frac{\textbf {u}\cdot\textbf {v}}{|\textbf {u}||\textbf {v}|}$
Step 2: $\cos\theta=\frac{\langle 4,3 \rangle\cdot\langle 1,5 \rangle}{|\langle 4,3 \rangle||\langle 1,5 \rangle|}$
Step 3: $\cos\theta=\frac{4(1)+3(5)}{\sqrt (4^{2}+3^{2})\cdot\sqrt (1^{2}+5^{2})}$
Step 4: $\cos\theta=\frac{4+15}{\sqrt (16+9)\cdot\sqrt (1+25)}$
Step 5: $\cos\theta=\frac{19}{\sqrt (25)\cdot\sqrt (26)}$
Step 6: $\cos\theta=\frac{19}{5\times\sqrt (26)}$
Step 7: $\cos\theta=\frac{19}{5\sqrt (26)}$
Step 8: $\theta=\cos^{-1}(\frac{19}{5\sqrt (26)})$
Step 9: Solving using the inverse cos function on the calculator,
$\theta=\cos^{-1}(\frac{19}{5\sqrt (26)})\approx41.8^{\circ}$
