1. **State the problem:** A farmer wants to build a fence around a right-angled triangular field. One angle is 53° and the side opposite this angle is 126 m. We need to find the total cost of the fence, given the cost is 1.24 per metre, and round the answer to the nearest pound. 2. **Identify the sides of the triangle:** The triangle has a right angle, so the sides are: - Opposite side to 53°: 126 m (given) - Adjacent side to 53°: unknown - Hypotenuse: unknown 3. **Use trigonometric ratios:** We use the sine and cosine functions to find the other sides. - Opposite side = 126 m - Angle = 53° Using cosine for adjacent side: $$\cos(53^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ Using sine for opposite side: $$\sin(53^\circ) = \frac{126}{\text{hypotenuse}}$$ 4. **Calculate the hypotenuse:** $$\text{hypotenuse} = \frac{126}{\sin(53^\circ)}$$ Calculate $\sin(53^\circ) \approx 0.7986$: $$\text{hypotenuse} = \frac{126}{0.7986} \approx 157.7 \text{ m}$$ 5. **Calculate the adjacent side:** $$\cos(53^\circ) = \frac{\text{adjacent}}{157.7}$$ Calculate $\cos(53^\circ) \approx 0.6018$: $$\text{adjacent} = 157.7 \times 0.6018 \approx 94.9 \text{ m}$$ 6. **Calculate the perimeter (total fence length):** $$\text{Perimeter} = 126 + 157.7 + 94.9 = 378.6 \text{ m}$$ 7. **Calculate the total cost:** $$\text{Cost} = 378.6 \times 1.24 = 469.46$$ 8. **Round to the nearest pound:** $$\boxed{469}$$ **Final answer:** The total cost of the fence is 469 to the nearest pound.