Find, correct to two decimal places, the acute angle between \(p = \begin{pmatrix} 13 \\ 14 \end{pmatrix}\) and \(q = \begin{pmatrix} 12 \\ 5 \end{pmatrix}\).

A.

23.52°

B.

24.50°

C.

29.52°

D.

29.82°

Correct answer is B

\(p . q = |p||q|\cos \theta\)

\(156 + 70 = (\sqrt{13^{2} + 14^{2}})(\sqrt{12^{2} + 5^{2}}) \cos \theta\)

\(226 = (\sqrt{365})(13) \cos \theta\)

\(\frac{226}{13\sqrt{365}} = \cos \theta\)

\(\cos \theta = 0.9099\)

\(\theta = 24.50°\)