T

he f

our corner

s

of this s

hap

e…

…come t

ogether

t

o make this.

finding missing angles

The angles of a four-sided shape add up to 360º

Squares and rectangles have four equal angles, a

quarter turn each, and even the most uneven four-

sided shape still has four angles adding up to 360º.

82º

103º

115º

60º

60º

115º

103º

82º

Let’s step the investigation up a gear! Find the mystery angles marked

on the crime scene diagram, a, b, c, d, e, f, and the all important angle,

g, which lets us work out the bounce angles.

Hint: it’s worth going in alphabetical order.

BULLET

PATH

MICKY

BENNY

FOOTPRINTS

BROKEN

GLASS

18º

CRIME SCENE SKETCH

CASE GEO180

(ANGLES AS MEASURED

BUT DRAWING NOT TO

SCALE)

72º

CHARLIE

FOOTPRINTS

28º

158º

TIRE

TRACKS

56º

aº

bº

cº

dº

eº

fº

gº

18º

you are here 4 35

sharpen solution

Let’s step the investigation up a gear! Find the mystery angles marked

on the crime scene diagram, a, b, c, d, e, f, and the all important angle,

g, which lets us work out the bounce angles.

BULLET

PATH

MICKY

BENNY

FOOTPRINTS

BROKEN

GLASS

18º

CRIME SCENE SKETCH

CASE GEO180

(ANGLES AS MEASURED

BUT DRAWING NOT TO

SCALE)

72º

CHARLIE

FOOTPRINTS

28º

158º

TIRE

TRACKS

56º

aº

bº

cº

dº

eº

fº

gº

18º

a)

28º

aº

a and 28º are complementary.

a + 28º = 90º, so a = 62º

b)

The room is a four-sided shape and the other three corners are right angles, so

b = 360º - (90º + 90º + 90º) = 90º

c)

62º

158º

cº

c is part of a four-sided shape, with aº

and the corner angle bº we just found, so

c = 360º - (158º + 62º + 90º) = 50º

36 Chapter 1

finding missing angles

d)

50º

dº

d is vertically opposite c, so d = 50º

e)

50º

eº

e forms a straight line with c, so

e = 180º - 50º = 130º

f)

130º

fº

f is vertically opposite e, so f = 130º

Since we believe that the bullet bounced in and out at equal

angles, what do you think these angles will turn out to be?

Is it possible to tell yet whether Charlie shot Micky?

g)

130º

18º

gº

g is part of a triangle with 18º and f, so

g = 180º - (18º + 130º) = 32º

32º

you are here 4 37

lining up the tire tracks

Great! We know these two angles should

be equal so we just do 180 minus 32…and

then divide by 2 to get 74 degrees!

Frank: Whoa. Not so quick—based on ballistics, that’s what

the angles should be, but that’s what we’re still trying to establish.

Jill: But how can we check it?

Frank: Well, it depends what angle the car was parked at,

doesn’t it? Remember, we can’t just say it “looks about right” on

the sketch.

Joe: But the car isn’t even marked on the sketch.

Jill: No, it isn’t. But we have the tire tracks—and the angle of

one of those. Though not the one on the side that the bullet hit.

Joe: That’s just typical! Why couldn’t they have measured the

angle of the other track?

Frank: I think it doesn’t matter which side they measured…

I’ve never seen a car where one set of tires was at a different

angle to the other side!

Jill: That’s true…so does that mean that both sets of tire marks

must be at the same angle?

Frank

Jill

BENNY

FOOTPRINTS

BROKEN

GLASS

TIRE

TRACKS

56º

Joe

38 Chapter 1

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