Find, correct to two decimal places, the acute angle between \(p = \begin{pmatrix} 13 \\
FURTHER MATHEMATICS
WAEC 2011
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: B. 24.50°
Explanation
\(p . q = |p||q|\cos \theta\)
\(156 + 70 = (\sqrt{13^{2} + 14^{2}})(\sqrt{12^{2} + 5^{2}}) \cos \theta\)
\(226 = (\sqrt{365})(13) \cos \theta\)
\(\frac{226}{13\sqrt{365}} = \cos \theta\)
\(\cos \theta = 0.9099\)
\(\theta = 24.50°\)
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