1. Yused Valentina Rodríguez
American Military Academy
Mentor: Natalia Santiago
Assistant mentor: Valerie Ann Carrasquillo
Universidad Metropolitana
Bio-Mathemathics

2. • Gigantic and Invisible right Triangles
• Inclinometer
• To measure the height of tall buildings, and the altitude of kites (or a
model rocket) using an inclinometer and basic properties of right
triangles.
• Questioning and Checking
Tangent
Opposite
Adjacen
t
• By using a gigantic
invisible right
triangle and an
inclinometer, it will
be possible to find
out the height (or
altitude) of the
given object.

3. Materials and Procedures used in the experiment.

4. 1. Inclinometer
2. Long tape measure; alternatives:
a. Pre-measured length of rope
b. Calibrated pedometer
3. Calculator; alternatives:
a. Tangent angle table
4. Building to measure
5. Lab notebook to record angles

5. 1. Make an inclinometer.
a. Download the inclinometer template file, and follow the
instructions
it contains to make your own inclinometer.
2. Choose the object to be measured.
3. Measure the distance between the building and the sight location.
4. Holding up the inclinometer, sight along its top line with the highest
point of the building.
5. Writing the angle given by the inclinometer, measure the building two
more times to get the average angle.
6. Calculate the height of the object by multiplying the base line length
with the measured angle’s tangent.
a/b = tan θ.

6. Plaza las Americas Office Building
San Patricio Plaza
Mercantil Plaza
Inclinometer

7. Object Baseline
(ft.)
θ1
(deg)
θ2
(deg)
θ3
(deg)
θavg
(deg)
Tan
θavg
Height
obtained
Actual
height
Error
Percenta
ge
Plaza las
Americas
Office
Building
147 ft. 55° 50° 59° 55° 1.3764 202 ft. 167 ft. 21.0%
San Patricio
Plaza
76 ½ ft. 27° 23° 21° 24° 0.4452 34 ft. 31 ft. 9.7%
Mercantil
Plaza
172 ft. 46° 55° 45° 49° 1.1504 198 ft. 185 ft. 7.0%
Molecular
Science
Research
Building
142 ft. 50° 49° 49° 49° 1.1504 163 ft. 134 ft. 22.0%

8. Discussions
• To create the base of the
triangle, a long tape measure
was used from the building to the
desired sighting location.
• That distance was recorded and
later used. The inclinometer was
used to record three angles of
inclination of the building.
• After this was done to all four
buildings, the average of the
three recorded angles (rounded
to the nearest degree) was
turned into its tangent and
multiplied by the base line. This
resulted in the height (rounded to
the nearest foot) of the building.
Conclusions
• The height obtained was
compared to the actual height
of the buildings.
• To get the error percentage, the
difference of both heights was
divided by the actual height and
then multiplied by one-hundred.
• Results showed it is possible to
calculate the approximate
height of a building with an
inclinometer, a right triangle,
and an average error
percentage of less than twenty
percent.

9. • In the future, I hope, that with the principals obtained with this
research investigation, I will be able to measure famous monuments
and buildings with unique architecture and find out how their
structure affects their height.
Al Kamiz Towers,
Dubai
Mesk Tower, Dubai Dubai Towers Dubai

10. • Andrew Olson, Ph.D., Gigantic, Invisible Triangles: Measuring Height
(or Altitude) with an Inclinometer, 2013-01-10, from:
http://www.sciencebuddies.org/science-fair-
projects/project_ideas/Math_p026.shtml#background
• Steve Seow, Professor Billy Wooten, Finding angle using Tangent,
2004-3-2, from:
http://www.stevenseow.com/tutorials/FindingAngleUsingTangent.html
• Jim Reed, Ratios in Right Triangles, 2002-05-30, from:
http://staff.argyll.epsb.ca/jreed/math9/strand3/3101a.htm

11. • Dr. Juan F. Arratia
• Natalia Santiago
• Anna C. Flores
• Valerie A. Carrasquillo
• Wanda Rodriguez
• AGMUS Institute of
Mathematics