The student can use ratios and proportions to make indirect measurements from scale drawings or similar figures. An example shows using similar triangles to find the height of a flagpole given the height and shadow of a stick. Another example shows using similar triangles to find the height of Reunion Tower by measuring the angle of reflection in a mirror and distances from the observer's perspective.

1. Indirect Measurement
The student is able to (I can):
• Use ratios to make indirect measurements
• Use scale drawings to solve problems.

2. indirect
measurement
Any method that uses formulas, similar
figures, and/or proportions to measure an
object.
Example: An 8 foot tall stick casts a
6 foot shadow. At the same time, a tall
flagpole casts an 18 foot shadow. How tall
is the flagpole?
6
8
18
x
The triangles are similar by AA~.
8 x
6 18
= 6x = 144 → x = 24 feet

3. Example Miriam saw a mirror on the ground and
noticed that she could see the top of
Reunion Tower in the mirror. Her line of
sight was 5’ above the ground, and the
mirror was 2’ away from her. She measured
the distance from that position to the
base of Reunion Tower, and it was 224 feet.
How high is Reunion Tower?
The reflection creates congruent angles, so
the triangles are similar by AA~.

4. Example
5’
2’ 224’
x
5 x
2 224
2x 1120
x 560 ft.
=
=
=