// maths › Forensics
A worked real-world example: from the horizontal travel and vertical drop between two marks, inverse tangent recovers the angle at which a projectile struck — the geometry behind trajectory and impact-angle reconstruction — shown on an animated scene you can adjust.
impact angle = tan⁻¹(vertical drop / horizontal travel)
A mind behind this: Hipparchus of Nicaea c. 190 – c. 120 BC
From two reference marks — where a projectile entered and where it struck — investigators measure the horizontal travel and the vertical drop between them. The inverse tangent of drop over travel gives the angle of impact.
Yes. The width-to-length shape of a blood drop gives an impact angle through an inverse-sine relationship, and directionality plus angles let analysts triangulate the origin point in three dimensions — the same trigonometric ideas.
Tangent turns a known angle into a side ratio; here the situation is reversed — the side lengths are measured and the angle is unknown — so the inverse tangent (arctan) is used to recover the angle from the ratio.
It gives a sound estimate when the reference points are clearly identified and measured accurately, but real projectiles can deflect or tumble, so analysts treat the result as one line of evidence among several.
Crime-scene reconstruction, ballistics, accident investigation and blood-spatter analysis all rely on impact angles to place a source or rebuild a sequence of events from physical marks alone.