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Head First 2D Geometry by Dawn Griffiths, Stray

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T
he rop
e is fixed t
o a
is closes
t t
o the
f
loor.
the end of the
rope—the height
a v
ery ta
ll per
son
needs when
swinging.
how much rope?
A longer rope swings further and lower
The wider the gap between the platforms, the more exciting the swing
will be—but there’s a catch. The TV company doesn’t just want the
widest swing, they want the widest possible swing without people
smashing into the floor!
Safety line
The floor
4m
2m
p
oint in the c
eiling here.
Comp
eti
t
or
s
tarts her
e.
In the middle of the
swing the comp
eti
t
or
T
his is the low
es
t
saf
e height f
or
2m
140 Chapter 3
If you’r
e stuck trying t
o design the skate cour
se
on page 133, then try this t
o get y
ou started.
the pythagorean theorem
So, before we can work out
anything else, we need to
quickly find how long the
rope can safely be, right?
What’s the longest the rope can be without going below the safety line?
Q:
The Pythagorean Theorem formula (c
2
= a
2
+ b
2
) looks
like it’s for finding the hypotenuse (c). But sometimes we’re
finding a length of a short side. How do I know what I’m
supposed to be finding and how to find it?
A:You can rearrange the formula to focus on one of the short
sides (legs). Like a
2
= c
2
– b
2
or b
2
= c
2
– a
2
, but the most reliable
thing to do is to focus on the meaning behind the pattern. If you’re
looking for the hypotenuse remember that the squares of the two
shortest sides add up to make the square of the longest side.
If you’re finding a short side then you need to think of the pattern
like this: the difference between the square of the longest side and
another side is the square of the remaining side.
Q:
OK, that’s not so bad when I’m given the lengths of
two sides and I have to find the other side’s length. But what
about when I’m only given one side and I have to find integer
values that complete a right triangle? The formula can’t give
me the answer because I don’t have enough values!
A:Again, think about the pattern behind the formula. If you’ve
got a load of possible values—or if you know the value is within a
range (like “less than 20”)—then here’s a trick you can rely on to
find the answers: just remember that this pattern is about square
numbers. (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…etc).
Write down all the values you’ve been given to choose between,
and then write down their squares. Then compare pairs of
numbers and see whether they add up to a square number, or
whether the difference between them is a square number.
you are here 4 141

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