WAEC Further Mathematics 2016 Paper

$\overset{\rightarrow}{r}\cdot \overset{\rightarrow}{t} = \left|\overset{\rightarrow}{r}\right| \left|\overset{\rightarrow}{t}\right| \cos \theta$

$\overset{\rightarrow}{r}\cdot \overset{\rightarrow}{t} = (3i + 4j) \cdot (-5i + 12j) = -15 + 48 = 33$

$\left|\overset{\rightarrow}{r}\right| = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5$

$\left|\overset{\rightarrow}{t}\right| = \sqrt{(-5)^{2} + 12^{2}} = \sqrt{169} = 13$

$\cos \theta = \frac{\overset{\rightarrow}{r}\cdot \overset{\rightarrow}{t}}{\left|\overset{\rightarrow}{r}\right| \left|\overset{\rightarrow}{t}\right|}$

$\cos \theta = \frac{33}{5 \times 13} = \frac{33}{65}$

$\theta = \cos^{-1} \left( \frac{33}{65} \right) \approx 59.5^{\circ}$