Gamma starts with a speed ratio: this toy triangle compares 3 m/s to a 5 m/s speed limit, so beta is the visible fraction 3/5. The numbers are deliberately small model inputs, not measured light-speed data; real velocity measurements would carry uncertainty before gamma is computed.
A slow toy speed limit turns beta and gamma into exact ratios. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Speed is compared to the limit
This book uses toy speed limit 5 m/s; real light speed is much larger. The toy speed is 3 m/s while the speed limit is 5 m/s, so beta is 3/5.