1. **State the problem:** We need to find the perimeter of a right-angled triangle with one angle of 43° and the side adjacent to this angle (base) measuring 13.8 m. 2. **Identify known values:** - Angle $A = 43^\circ$ - Base $b = 13.8$ m - Right angle at $C = 90^\circ$ 3. **Find the other sides:** Let the hypotenuse be $c$ and the opposite side to angle $A$ be $a$. Using trigonometric ratios: $$\cos A = \frac{b}{c} \implies c = \frac{b}{\cos A} = \frac{13.8}{\cos 43^\circ}$$ Calculate $\cos 43^\circ \approx 0.7314$: $$c = \frac{13.8}{0.7314} \approx 18.86 \text{ m}$$ 4. Find the opposite side $a$ using sine: $$\sin A = \frac{a}{c} \implies a = c \sin A = 18.86 \times \sin 43^\circ$$ Calculate $\sin 43^\circ \approx 0.6820$: $$a = 18.86 \times 0.6820 \approx 12.86 \text{ m}$$ 5. **Calculate the perimeter $P$:** $$P = a + b + c = 12.86 + 13.8 + 18.86 = 45.52 \text{ m}$$ 6. **Round to 1 decimal place:** $$P \approx 45.5 \text{ m}$$ **Final answer:** The perimeter of the triangle is approximately **45.5 m**.