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Extra Credit Project
Similar Triangles in Everyday Situations
__________________________________________________________
Created by:
Carolina Jaramillo Period 1
Introduction
• Using proportions derived from similar triangles, I will find the height of the very top of my house.
HOW WILL I DO THIS ?
I will place a mirror on the floor between the object and me and look into it from a specific distance from
which I can view the top of the object clearly.The distances involved will be the make-up of the
proportions.
Heig
ht
of
house
Distance between object and mirror
Distance between mirror and me
My h
eig
ht
?
Why can I use these two triangles to set up a proportion?
• Knowing about similar triangles and their shortcuts, I could use the Angle-Angle-Similarity Theorem to make sure that these two triangles are similar.
•I know that <C and <O are congruent because they both are right angles and, believe it or not, ALL right angles are congruent.
•Also, I know that <FAC and <EAO are congruent because mirrors reflect off light at the same angle that light hits it.
•Therefore: ΔFCA ~ ΔEOA
O
E
F
AC
F
AO
E
C
Using the statement ΔFCA ~ ΔEOA, I will set up a proportion in which the corresponding sides will
be in place. I will use “x” in the proportion to denote the height of
my house.
My height corresponds to the house’s height. My distance from
the mirror corresponds to the house’s distance from the mirror.
My height = Me to mirror
House’s height House to mirror
Measuring Distances
I went outside and took my 2-foot ruler to begin my measuring...
mirror
me
ruler
notes
More measurements!
As I continued my measurements...
...my doggy slept!
ZZZZZZZZ...
...later, he woke up to watch me
What in the dog-world is she
measuring???
That project looks hard...
That’s too much math for
me...
Anyway…
getting back to the project…
♫ Plug it in, Plug it in ♫ …
My height = Me to mirror
House’s height House to mirror
57 = 31 x 264
Substitution
Now, cross-multiply and come up with a simple equation:
57(264) = 31(x)Simplify 15048 = 31x
485.4193548 = x
Division Prop. of equality
485 inches = x
Round
***Note: all measurements are in inches
• As you saw, I used a proportion to find the height of my house.
Height: About 485 inches
-or- about 40 feet
The End