Head First 2D Geometry

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?

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