Similar Triangles word problems and applications in the real world.

1. Image Source: http://www.canon.com

2. Image Source: http://www.olympusamerica.com

3. Image Source: http://www.canon.com

4. Image Source: Dirt River Radio Band Photos taken by Passy
Why does a low light Zoom Camera Lens cost a lot of money?
Because it has a lot of very precisely shaped movable geometrically
shaped optics inside it, which all have to be mathematically perfect
in their shape and movement.
Lots of precise work to make, means lots of $ on the price tag.

5. Image Source: http://www.rags-int-inc.com
Similar Triangle “Bow Tie” mathematics is involved with Optics
Eg. Camera Lenses and Eyes Glasses.

6. S.F. = 24 / 8 = 3
Therefore L = 3 x 5
L = 15
Because A = D we know that AB is parallel to DE (Alternates)
The two angles each side of “C” are Equal (Vertical Angles)
B = E by Alternates, or because total triangle = 180
THEREFORE TRIANGLES ARE SIMILAR BY AAA RULE.
A
C
B
D
E
5
24
8
L = ?

7. 24 L
8 5
We can also use proportion of matching sides:
A
C
B
D
E
5
24
8
L = ?
= Set up the sides and
then Cross Multiply
24 x 5 = L x 8
120 = 8L Solve this equation by dividing by 8
15 = L or L = 15

8. A
C
ED
B
4
8
10
L = ?
Calculate the length “L” of DE
Scale Factor = 8 / 4 = 2
Because of Similarity,
AC corresponds to CE
AB corresponds to DE
Because they are
matching sides.
DE = 2 x 10
L = 20
ABC ~ CDE by AAA
Vertical Angles at Point C

9. Similar Triangles are used to
determine the Height of tall
objects using shadow lengths.
Diagrams for these questions have Triangles inside Triangles
h = ?
2m
12m
84m

10. ABC and ADE share common A
They also each have a Right Angle
ABC ~ ADE (by AAA)
Next step is to find the Scale Factor, and then use it to get “h”
h = ?
2m
12m
84m
A
B
C E
D

11. S.F. = AE / AC
S.F. = 84 / 12
S.F. = 7
2m
12m
C E
h = ?
84m
A
B
D
The large triangle is Seven Times bigger than the small one
So the Height of the Tree is 7 times the height of the person.
h = 7 x 2 = 14m

12. 2m
12m
C E
h = ?
84m
A
B
D
h 84
2 12=
h x 12 = 84 x 2
12h = 168 h = 14m
Set up the sides and
then Cross Multiply
Solve by dividing by 12
We can also work
out this question
by setting up the
Ratios and then
Cross Multiplying.

13. Redraw this diagram and use
Similar Triangles on the shadow
Lengths to work out the Height
of the mobile phone tower .
Draw the standard Triangles inside Triangles Diagram
h = ?
1.8 m
6m
60m

14. ABC ~ ADE (by AAA)
S.F. = 60/6 = 10
h = 10 x 1.8
h = 18m
We have found the Scale Factor, and then used it to get “h”
h = ?
1.8m
6 m
60m
A
B
C E
D

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