Finding the Angle

Turn s = rθ round and it gives the angle: $\theta = \frac{s}{r}$, in radians. A swing of radius 8 m whose seat travels 12 m along its arc turns through 12/8 = 1.5 radians.

For degrees, multiply by $\frac{180^{\circ}}{\pi}$: $\frac{1.5\cdot 180^{\circ}}{\pi}$ is about 85.9°. The two steps can share one line: θ = 12/8 × 180°/π.

Sanity check: 1.5 radians is a little less than π/2, about 1.57, so the answer should be a little less than 90°. It is.