Triangulation

1
Triangulation

• What it is Why we Use It
• Geometry Review
• Applying Geometry

2
What it is Why we Use It

• Triangulation is a process that uses geometry to
  indirectly measure distances.
• Used when the object being measured cannot be
  measured directly
• Too large, inconveniently located

3
Geometry Review

• Similar Triangles
• Corresponding angles are congruent
• Ratio of any two corresponding sides or altitudes
  are equal
• The above ratios tell us how many times bigger or
  smaller the triangles are to one another

4
Applying Geometry (1 of 3)

• Making Similar Triangles
• First line extends from eye to top of
  object
• Second line extends from eye to bottom of object
• Do you see the two triangles?
• The small triangle is Red
• The large triangle is Green

5
Applying Geometry (2 of 3)

• These triangles are similar because they share
  one angle and the ruler is parallel to the wall
• Because these are similar triangles we can use
  any two corresponding sides or altitudes to
  calculate the scale
• We measured the lengths below

6
Applying Geometry (3 of 3)

• Once we have the scalewe can convert
  anydistance in one triangle to the
  corresponding distance in the other triangle
• The wall appears to be 28.3 cm tall on the meter
  stick
• Use the Scale to convert from small to large

7
Practice Problem
Step 1 Draw label a diagram In this case, we
will need to picture the scenario from the side.
9.30mL

• Julia is standing across a river from her house
  and is wondering exactly how far away she is.
  She holds up a ruler vertically, 47.81 cm from
  her eye, and measures the apparent height of the
  house to be 9.32 cm. If the actual height of the
  house is 9.30 m, how far away is Julia standing?

Step 2 Define the scale
Step 3 Perform the conversion.