1. **State the problem:** We have a right triangle with a right angle at vertex P. Angle at P is 51.2°. The side adjacent to this angle (next to 51.2°) is 124 m. We want to solve for the side opposite the angle, labeled $n$, and the hypotenuse $p$. 2. **Relevant formulas:** In a right triangle, the trigonometric ratios are: - $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ - $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ - $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ 3. **Find the hypotenuse $p$ using cosine:** $$\cos(51.2^\circ) = \frac{124}{p}$$ Multiply both sides by $p$: $$p \cos(51.2^\circ) = 124$$ Divide both sides by $\cos(51.2^\circ)$: $$p = \frac{124}{\cos(51.2^\circ)}$$ 4. **Calculate $p$ numerically:** $$p = \frac{124}{\cos(51.2^\circ)} \approx \frac{124}{0.627} \approx 197.8$$ 5. **Find the opposite side $n$ using tangent:** $$\tan(51.2^\circ) = \frac{n}{124}$$ Multiply both sides by 124: $$n = 124 \times \tan(51.2^\circ)$$ 6. **Calculate $n$ numerically:** $$n = 124 \times 1.234 \approx 153.0$$ **Final answers:** $$p \approx 197.8 \text{ m}$$ $$n \approx 153.0 \text{ m}$$