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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