1. **State the problem:** Calculate the size of angle BAC in each right-angled triangle using the tangent ratio. 2. **Recall the formula:** For a right triangle, \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \). 3. **Triangle i:** - Given opposite side = 4, adjacent side = 5. - Calculate \( x = \tan^{-1} \left( \frac{4}{5} \right) \). - Using a calculator, \( x = 38.7^\circ \) (to 1 decimal place). - Therefore, \( \angle BAC = 38.7^\circ \). 4. **Triangle ii:** - Given opposite side = 8, adjacent side = 3. - Calculate \( x = \tan^{-1} \left( \frac{8}{3} \right) \). - Using a calculator, \( x = 69.4^\circ \) (to 1 decimal place). - Therefore, \( \angle BAC = 69.4^\circ \). **Final answers:** - Triangle i: \( 38.7^\circ \) - Triangle ii: \( 69.4^\circ \)