1. Problem: Determine the size of the angle BAC in a right triangle where the hypotenuse AC is 16 cm and the base BC is 8 cm. 2. In a right triangle, use cosine to find the angle because cos \(\theta\) = adjacent/hypotenuse. 3. Here, adjacent side BC = 8 cm and hypotenuse AC = 16 cm, so $$\cos \theta = \frac{8}{16} = 0.5$$ 4. Find angle \(\theta\) by taking the inverse cosine: $$\theta = \cos^{-1}(0.5)$$ 5. Using a calculator, \(\cos^{-1}(0.5) = 60^\circ\) 6. Therefore, \(\angle BAC = 60^\circ\).