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Head First 2D Geometry by Dawn Griffiths, Stray

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T
op-down vi
ew of the
assessing the crime scene
Do the angles between Benny, Micky,
and the bullet match up?
At the crime scene, the investigators took some measurements
and sketched the positions of Benny, Micky’s body, and the point
where they found the bullet in the wall, all relative to the building
where the crime took place.
cr
ime sc
ene
CRIME SCENE SKETCH
PLAN VIEW
CASE GEO180
(ANGLES AS MEASURED
BULLET FOUND
BUT DRAWING NOT TO
STUCK IN WALL HERE
SCALE)
BULLET
PA
TH
DOOR
MICKY
BENNY
FOOTPRINTS
18º
81º
86º
(CHALK OUTLINE
OF HIS BODY)
They must have been busy that day, because
they didn’t measure everything! But, they
found one important detail: the bullet
entered the wall at an angle of 18º through
the front wall.
So, to solve the crime, all you have to do is
prove that from where Benny was standing
to the target (Micky), the bullet would have
traveled in a straight line that joins up
perfectly with the bullet path.
BULLET
PA
TH
MICKY
BENNY
18º
T
he line Benn
y w
ould
aim down to hi
t Mick
y.
How the bullet was
trav
eling when it
hi
t the w
a
ll.
If Benny shot Mick
y, these
t
wo line segments mus
t join up
t
o make a s
traight line.
Chapter 1 4
finding missing angles
Well, this is easy! You can see just
by looking at it that the line from
Benny to Micky and the line for the bullet
path join up to make one straight line.
Jill: Hang on—I’m not sure we can really go by eye like that!
Joe: Oh, well, we could use a ruler to check it. But I’m pretty
sure it’s a straight line.
Frank: I don’t think we could trust it, even if the ruler
showed it was straight—the sketch clearly says “drawing not
to scale.” The angles we’ve been given are correct, but if you
checked it with a protractor the lines on the sketch wouldn’t
necessarily be the same angles as at the scene itself.
Joe: What? Well, it’s useless then, isn’t it?
Frank: It’s not useless—if it says 18º on the sketch then it
was 18º at the scene because they measured it there. But I
don’t think we can go on what the sketch looks like. We’re
going to actually have to work out whether the line segments
really join up into one straight line.
Joe: But we’ve only got three angles to go on. I bet the chief
will say we need to fill them all in. He’s gonna be mad.
Jill: What if we could find a way to guess some angles based
on other angles or something? But that just sounds really
inaccurate—not exactly good for our case in court!
Frank: It sounds like the right kind of approach though. And
anyway, I think they’ve measured five angles, not just three.…
Frank
Jill
Joe
Does the sketch tell you five angles, or just three?
Is there a way you could start to find some of the angles you haven’t
been given on the sketch?
you are here 4 5

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