Use ratios to make indirect measurements Use scale drawings to solve problems.

1. Obj. 37 Proportional Relationships
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?
x
8
6
18
The triangles are similar by AA~.
8 x
6x = 144 → x = 24 feet
=
6 18

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

5. Example
According to the map’s scale, 1 in = 100 mi.
If it measures 2.75 in. from Ft. Worth to
San Antonio, how far away are the two
cities?
1
2.75
=
100
x
x = 275 mi.