Answer
$36.87^{\circ}$
Work Step by Step
Step 1: We let $\textbf {u}=\langle 1,7 \rangle$ and $\textbf {v}=\langle 1,1 \rangle$
Step 2: The formula for finding the angle between a
pair of vectors is $\cos\theta=\frac{\textbf {u}\cdot\textbf {v}}{|\textbf {u}||\textbf {v}|}$
Step 3: $\cos\theta=\frac{\langle 1,7 \rangle\cdot\langle 1,1 \rangle}{|\langle 1,7 \rangle||\langle 1,1 \rangle|}$
Step 4: $\cos\theta=\frac{1(1)+7(1)}{\sqrt (1^{2}+1^{2})\cdot\sqrt (7^{2}+1^{2})}$
Step 5: $\cos\theta=\frac{1+7}{\sqrt (1+1)\cdot\sqrt (49+1)}$
Step 6: $\cos\theta=\frac{8}{\sqrt (2)\cdot\sqrt (50)}$
Step 7: $\cos\theta=\frac{8}{\sqrt (2\times50)}$
Step 8: $\cos\theta=\frac{8}{\sqrt (100)}$
Step 9: $\cos\theta=\frac{8}{10}$
Step 10: $\theta=\cos^{-1}(0.8)$
Step 11: Solving using the inverse cos function on the calculator,
$\theta=\cos^{-1}(0.8)\approx36.87^{\circ}$
