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Trigonometric Equations
Mathematical relationship between blood stain and angle of impact
A
E
F
E’
B
A’
B’
F’
A,B, E, F = four points on the surface of sphere (blood drop in space)
A’,B’, E’, F’ = same four points projected on a surface in the form of a blood stain
E’ to F’ = width (w) of blood stain
A’ to B’ = length (l) of blood stain
blood drop in space (assume spherical) therefore EF = AB
1
Determination of Point of Origin in Space
A
B

D
A
’
B
’
pt of origin in space
Z

Y
Solve for the length of Z (D to B). hint:  (angle of impact) is known,
and Y is given.
2
Process for determining spatial origin of blood source
1. Bisect at least three (3) blood droplets that will result in a point of intersection (PI) &
label each droplet respectively i.e., S1, S2, S3, etc.
2. Using calipers, measure width & length of each droplet identified in the previous
step.
3. Determine angle of impact of each of the blood spots (sine function)
Sine = O/H = W/L = angle of impact
4. Measure distance (Y) of blood drop to PI for each droplet.
5. Determine Z (distance from floor or wall) using tangent function
Tangent = O/A = Z/Y or Z = tangent * Y
6. String distance using appropriate materials
Experiment #4: Blood Stain Address Lab
Purpose: Determine the address of the blood source given blood spatter evidence
Materials:
Ruler
String
Trig calculator
Calipers
Ring stand
Protractor
Blood spatter evidence
Procedure:
1. Construct the data on a separate sheet of paper (see below).
2. Locate a series of blood droplets that can be measured (W & L) and have a common
point of intersection (PI). Tape 2 additional pieces of paper to the sheet to bisect.
3. Line up the droplet w/ a ruler so it bisects (runs down the middle) the drop.
4. Once aligned, draw a pencil line starting through the droplet to the “PI” (this will
need to be estimated). Repeat this process for other blood droplets until the point of
intersection (PI) or line of convergence is established.
5. Using calipers measure the width and the length of each identified droplet (0.01 cm)
6. Divide the width by the length and record (Remember sine = O/A = W/L = of
impact). Using a calculator, determine the angle of impact and record in table.
7. Measure the distance (cm) from the droplet to the PI and record.
8. To determine Z (position in space) = tangent of  impact * Y (distance from the
droplet to the PI ). Repeat for the other spots and record.
9. Once all the calculations have been performed, string the flight path of the droplets to
determine the origin in space. Use the protractor the set the angle then tie a string
onto the ring stand (or use tape) to secure it.
3
spot #
W (cm)
L (cm)
W/L
angle impact (sine)
Y (cm)
Z (cm)
Y = distance from base of individual droplets to the PI
figure 1
blood spots at crime
scene
figure 2
bisect blood droplets
& draw a line to the
PI
PI
figure 3
measure and record
the width & length of
each blood droplet
S1
S2
L
PI
W
L
figure 4
measure distance
from droplet to PI
S2
Y1
S1
PI
Y2
4