Suppose the width of your fist is 5.9 inches and the length of your arm is 26.9 inches. Based on these measurements, what will be the angular width (in degrees) of your fist held at arm’s length?

Answer 1

We can use trigonometry to solve this. Width of fist = 5.9", but we have to cut that in half by drawing a perpendicular line to the center of the fist. This creates a right triangle with adjacent side = 26.9" and an opposite side = 5.9"/2 = 2.95". We know that tan θ = opposite side / adjacent side = 2.95 / 26.9 = 0.109665. So tan^-1 (0.109665) = θ = 6.25°. Lastly, we need to double this to get the whole angle for the width of your fist at 26,9". Answer: 12.5°.