(a) \(\cos x = 0.7431\) \(x = \cos^{-1} (0.7431)\) \(x = 42°\) (i) \(2 \sin x = 2 \sin 42\) = \(2 \times 0.6692\) = \(1.3384\) (ii) \(\tan \frac{x}{2} = \tan \frac{42}{2}\) = \(\tan 21°\) = \(0.3839\) (b) Sum of the interior angles of a polygon = \((2n - 4) \times 90°\) For a pentagon, n = 5 \((2(5) - 4) \times 90° = 6 \times 90°\) = \(540°\) Ratio of sides = 2:3:4:4:5 Total = 2 + 3 + 4 + 4 + 5 = 18 Largest angle = \(\frac{5}{18} \times 540° = 150°\)