1. **Problem statement:** We need to find the height $n$ of a flagpole given a right triangle where the angle between the wire (hypotenuse) and the ground is $72^\circ$, and the horizontal distance (adjacent side) is 2.8 m. 2. **Formula and explanation:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}.$$ Here, the wire is the hypotenuse, the ground is adjacent, and the flagpole height $n$ is the opposite side. 3. Since we want the height $n$ (opposite side), we use the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}.$$ We know the adjacent side (2.8 m) and angle $72^\circ$, so first find the hypotenuse $h$ using cosine: $$\cos(72^\circ) = \frac{2.8}{h} \implies h = \frac{2.8}{\cos(72^\circ)}.$$ 4. Calculate $h$: $$\cos(72^\circ) \approx 0.3090,$$ $$h = \frac{2.8}{0.3090} \approx 9.06 \text{ m}.$$ 5. Now find the height $n$ using sine: $$n = h \times \sin(72^\circ),$$ $$\sin(72^\circ) \approx 0.9511,$$ $$n = 9.06 \times 0.9511 \approx 8.61 \text{ m}.$$ 6. **Final answer:** The height of the flagpole is approximately **8.6 m** to 1 decimal place.