O'Reilly logo

Head First 2D Geometry by Dawn Griffiths, Stray

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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
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
18º
a)
28º
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
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
d is vertically opposite c, so d = 50º
e)
50º
e forms a straight line with c, so
e = 180º - 50º = 130º
f)
130º
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
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

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required