Similar Triangles Activity
Names:
A mirror placed on the ground can be used to indirectly measure the height of objects. When the mirror is placed at a
particular distance from the object (Do), then the distance that an observer stands from the mirror (Du) determines the
reflection that the observer will see in the mirror. During this activity, each group will be measuring various distances
OUTSIDE to determine the height of several objects (Ho). (Hu is the eye-level of the observer.)
Example: Height of a Flagpole
Ho
Hu = 5 ft 6 in
Do = 25 ft
2in
Proportion used to find height:
9 ft
Du =
(mirror)
Ho =
Directions: Fill in the missing information for each set of triangles, and then calculate the height of each object using a
proportion. Measurements will be taken to the nearest inch, and final answers will be rounded to the nearest tenth of a
foot.
.
Station 1:
Station 2:
Ho
Ho
Hu =
Hu =
Do =
Du =
name (
of observer
)
Do =
Du =
Proportion used to find height:
Proportion used to find height:
Ho =
Ho =
Station 3:
)
name (
of observer
)
Station 4:
Ho
Ho
Hu =
Hu =
Do =
name (
of observer
in
Du =
name (
of observer
)
Do =
Du =
Proportion used to find height:
Proportion used to find height:
Ho =
Ho =
Similar Triangles Activity
Names:
Station 5:
Station 6:
Ho
Ho
Hu =
Hu =
Do =
Du =
name (
of observer
)
Do =
Du =
Proportion used to find height:
Proportion used to find height:
Ho =
Ho =
name (
of observer
Application: Suppose you threw a Frisbee and it landed on your roof, caught in the rain gutter. You want to know
how high off the ground it is to the rain gutter to determine if a 12-foot ladder will suffice. You walk ten feet away
from the house to place your mirror on the ground, and then walk another five feet until you see the gutter in the
mirror.
(a) Draw a picture that represents this scenario.
(b) How high off the ground is the gutter if it is five feet six inches to your eye level?
(Show proportion)
(c) Using the answer from part (b), determine how far back from the house
your Dad would have to walk to see the same spot in the mirror, given
he is seven inches taller than you.
(d) Will the 12-foot ladder suffice if the ladder will hit the roof 9 inches from the top of the ladder, and the base of the
ladder is 3 feet away from the line of the gutter? Explain. Include a diagram with your solution.
WORK:
ANSWER:
)
Similar Triangles Activity
Names:
Teacher page (do NOT print)
Things to remember:
 9 feet 2 inches is not 9.2 feet. Have students work with more decimal places to ensure accuracy.
 Use groups of three– observer, measurer, and recorder. Each person in the group does one job twice, and
then they switch roles.
 If only 5’ tape measures are available, the large distances are harder to measure, and will elicit more error.
Request 50’ field tapes from coaches early (or get inexpensive 25’ tape measures from a store.)
ANSWERS
Example:
x
x
5 .5

25 9.17
x  15 ft
x
66in

300in 110in
x  180in  15 ft
5’6”
9’2”
25’
Application:
5’6”=5.5 ft
(b)
(c)
5.5 ft
x
5 ft
10 ft
x 5.5

10 5
x  11 ft
5’6”+7”=6’1” =6.0833 ft
6.0833 ft
11 ft
10 ft
y
11 6.0833

10
y
y  5.53 ft
(Dad is a bit more than ½ foot further back)
(d) According to OSHA, “Non-self-supporting
ladders, which must lean against a wall or other
support, are to be positioned at such an angle that the
horizontal distance from the top support to the foot of
the ladder is about 1/4 the working length of the
ladder.”
9 in
11 ft 3 in
**Overhang distance ignored for this example, but
can be incorporated for an additional challenge.
- 3 ft -
a b  c
3  h  11.25
2
2
2
2
2
2
h  10.84 ft
The gutter is above this mark so the ladder will NOT suffice.