1. **State the problem:** We need to find the perimeter of a right-angled triangle where one angle is 43° and the side adjacent to this angle (the base) is 13.8 m. 2. **Identify known values:** - Angle $A = 43^\circ$ - Side adjacent to angle $A$, $b = 13.8$ m - Right angle at the other corner, so the triangle has angles $90^\circ$, $43^\circ$, and $47^\circ$ (since $90 + 43 + 47 = 180$) 3. **Use trigonometric ratios:** Since $b$ is adjacent to angle $A$, we can find the hypotenuse $c$ using cosine: $$\cos(43^\circ) = \frac{b}{c} \implies c = \frac{b}{\cos(43^\circ)}$$ Calculate $c$: $$c = \frac{13.8}{\cos(43^\circ)}$$ 4. **Calculate the opposite side $a$:** Use sine: $$\sin(43^\circ) = \frac{a}{c} \implies a = c \times \sin(43^\circ)$$ 5. **Calculate values:** $$\cos(43^\circ) \approx 0.7314$$ $$c = \frac{13.8}{0.7314} \approx 18.86$$ $$\sin(43^\circ) \approx 0.6820$$ $$a = 18.86 \times 0.6820 \approx 12.86$$ 6. **Find the perimeter $P$:** $$P = a + b + c = 12.86 + 13.8 + 18.86 = 45.52$$ 7. **Round to 1 decimal place:** $$P \approx 45.5$$ m **Final answer:** The perimeter of the triangle is approximately **45.5 m**.