1. **State the problem:** A farmer wants to build a fence around a right-angled triangular field. One side adjacent to the right angle is 151 m, and the angle opposite this side is 52°. We need to find the total cost of the fence, given the cost is 1.42 per metre, and round the answer to the nearest pound. 2. **Identify the sides:** The triangle has a right angle, one side of length 151 m, and an angle of 52° adjacent to that side. Let's label the sides: the side of 151 m is adjacent to the 52° angle, the right angle is 90°, and the other angle is 38° (since angles in a triangle sum to 180°). 3. **Find the other two sides:** - Let the side opposite the 52° angle be $a$. - The side adjacent to 52° (given) is $b = 151$ m. - The hypotenuse is $c$. Using trigonometric ratios: $$\sin(52^\circ) = \frac{a}{c} \Rightarrow a = c \sin(52^\circ)$$ $$\cos(52^\circ) = \frac{b}{c} \Rightarrow c = \frac{b}{\cos(52^\circ)} = \frac{151}{\cos(52^\circ)}$$ Calculate $c$: $$c = \frac{151}{\cos(52^\circ)} \approx \frac{151}{0.6157} \approx 245.2 \text{ m}$$ Calculate $a$: $$a = 245.2 \times \sin(52^\circ) \approx 245.2 \times 0.7880 \approx 193.1 \text{ m}$$ 4. **Calculate the perimeter:** $$P = a + b + c = 193.1 + 151 + 245.2 = 589.3 \text{ m}$$ 5. **Calculate the total cost:** $$\text{Cost} = P \times 1.42 = 589.3 \times 1.42 \approx 836.0$$ 6. **Round to the nearest pound:** $$\boxed{836}$$ The total cost of the fence is 836 to the nearest pound.