How do you calculate the impact angle from a bloodstain's shape?

How do you calculate the impact angle from a bloodstain's shape?

• A. theta = arctan(width/length)
• B. theta = arcsin(width/length)
• C. theta = arccos(width/length)
• D. theta = width/length

Answer: (B)

When a droplet hits a surface at an angle, the stain becomes an ellipse. The width across the stain and the length along its longest axis encode how oblique the impact was. The geometry of the projection tells us sin of the impact angle equals the width divided by the length. So to get the angle, you take the inverse sine: theta = arcsin(width/length). This makes intuitive sense: a circular stain (width equals length) corresponds to a perpendicular impact (90 degrees), while a very elongated stain (width much smaller than length) comes from a shallow, glancing impact (a small angle). Using arctan or arccos would mix up the relationships and give an incorrect angle for this context.

When a droplet hits a surface at an angle, the stain becomes an ellipse. The width across the stain and the length along its longest axis encode how oblique the impact was. The geometry of the projection tells us sin of the impact angle equals the width divided by the length. So to get the angle, you take the inverse sine: theta = arcsin(width/length). This makes intuitive sense: a circular stain (width equals length) corresponds to a perpendicular impact (90 degrees), while a very elongated stain (width much smaller than length) comes from a shallow, glancing impact (a small angle). Using arctan or arccos would mix up the relationships and give an incorrect angle for this context.