triangle properties

Special O

er

60% o!

$750

SCREEN WAREHOUSE

Only slightly damaged, these screens still present a

crystal clear image but with uneveness in the viewable

range to each side.

28 31

30

Web ad f

or the

sp

ecia

l offer

screens

Will the special offer screen still do the job?

The screen is suitable if the viewable range (r) reaches

all the way to the back—but you only have the sides

given on the specification in the ad.

25

28 31

30

r ?

you are here 4 193

What technique from your Geometry Toolbox can help you find

the screen’s viewable distance, r?

Alti

tude

a

2

+ x

2

= 28

2

And this here

a

2

+ y

2

= 31

2

a new tool for your geometry toolbox

What technique from your Geometry Toolbox can help you find

the screen’s viewable distance, r?

The Pythagorean Theorem

It’s the right answ

er, but i

t’s a

lso

a w

orld of pain…so hold tight f

or

a new t

ool for y

our t

oolbox!

The screen viewing area is a scalene triangle

This means that when you add an altitude, it doesn’t bisect

the base. Instead of creating two nice, neat congruent right

triangles, you get two different right triangles. And you don’t

know the base of either of them!

So w

e’d need to

sol

v

e this her

e

28

31

28

31

a a

All three sides

are different

lengths.

x y

30

The two right triangles still work with the Pythagorean

Theorem, and we know that x and y together make 30 (but

aren’t equal to each other) so we could figure this out with a set

of three simultaneous algebra equations. If that sounds bad,

it kinda is. Don’t go there. But in case you’re tempted, here’s

how it starts out:

Plus, x and y ar

en’t jus

t ha

lf of 30!

a

2

+ x

2

= 28

2

a

2

+ y

2

= 31

2

x + y = 30

(a

2

+ x

2

= 28

2

)

- (a

2

+ y

2

= 31

2

)

3 equations

DANGER

do not cross this line

by subtraction

x

2

- y

2

= 28

2

- 31

2

x + y = 30, so x = (30 - y) (30 - y)

2

- y

2

= 28

2

-31

2

by substitution

Now…expand this out....

194 Chapter 4

triangle properties

Wouldn’t it be dreamy if there was a

way to find the height of a scalene triangle

without simultaneous equations? But I know

it's just a fantasy....

you are here 4 195

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