Externship Classroom Activity
Name: Teoyolli Luna
Date:
Contact Info: E-mail lunat@svusd.org
Phone: 949-770-8436
School: _Laguna Hills High School
Grade Level:_9th-12th
Duration: 1 and ½ periods for each activity Subject: Geometry
Pathway: Surveying (Engineering Technology Pathway)
Title of project: Indirect Measurement: Using Trigonometry and Surveying Techniques
Description of Activity
Activity #1: Students used small mirrors and tape measures to estimate the height of a tall object. Some
chose the flag pole, light post, or building on campus. Students gathered their data and used similar triangles
to determine the height of the object. They completed a poster showing all their calculations and drawings of
triangles.
Activity #2: Students made a clinometer (surveying tool used to measure angles) using a protractor, straw,
string, and paper clips. The clinometer was used to estimate the height of the same object they selected for
the first activity. They used their knowledge of right triangles and trigonometry along with the clinometer for
their measurements and calculations. The students then compared the results of the two different methods.
At the conclusion of these activities the student will be able to:
1. Know how to make and use a surveying tool (clinometer).
2. Solve a practical problem, like how to measure the height of inaccessible objects, just like surveyors
do.
3. Apply knowledge of similar triangles and trigonometry to solve problems.
4. Recognize and understand that there is a relationship between abstract math concepts and real-world
applications.
5. Review the Pythagorean Theorem.
6. Review the concepts of area and perimeter.
7. Set up and solve proportions involving similar triangles.
8. Work cooperatively with a partner to solve a practical problem.
ROCP/ High School or Community College course title
Course: Geometry
Projected Learning Outcomes for externship: Students will learn that abstract math concepts have
practical applications. They will learn how surveyors measure inaccessible objects.
Final Learning Outcomes (project completion): The students not only learned how math is used in an
actual career, they also had fun. The activities were all hands-on, something we seldom do in math
courses. The students learned how to make a clinometer with simple objects. They also learned how to
use the clinometer to measure tall objects around campus. Students also used mirrors and tape
measure to calculate a 2nd estimate of the height of the objects. They compared their results and
provided explanations for any discrepancies. Lastly, students learned and reviewed similar right
triangles, trigonometry, area, and perimeter.
Directions: What are the step-by-step directions that another educator would follow to
duplicate this activity:
Activity #1: Using Mirrors to Measure Objects Indirectly. Step 1: Each pair of students will need a tape
measure and small mirror. Step 2: Review the following concepts: angle of incidence = angle of reflection;
the Angle-Angle Postulate allows us to determine that 2 triangles are similar; similar triangles have
proportional sides. Step 3: Go outside and select an object which cannot be measured directly, for example,
a light post, a flag pole, or a tall building. Step 4: Place the mirror on the floor and practice seeing the
reflection of the top of the flag pole, light post or building. Step 5: Recognize that a triangle is formed from
your standing position to your eyes to the reflection of the mirror (see sketch in lesson plans). A second
similar triangle is formed from the position of the object to its highest point to the mirror. Step 6: Measure
all necessary distances (see sketch in lesson plans). Step 7: Using your measurements, set up a proportion
and solve for the unknown, the height of your object.
Activity #2: Using a Clinometer to Measure Objects Indirectly. Step 1: Make a clinometer using a
protractor, straw, string and paper clip (see lesson plans for details). Step 2: Learn how to use the clinometer
to measure angles. Step 3: Review trigonometric ratios (tangent, sine, cosine). Step 4: Go outside and use
the clinometer to measure the height of the object selected for the first activity. Step 5: Measure the
necessary distances (see lesson plans). Step 6: Create a poster showing all calculations and diagrams of how
the height was estimated.
Academic and Career & Technical Education Standards addressed in this exercise:
Geometry Standards: (5.0) Students prove that triangles are congruent or similar and are able to use the
concept of corresponding parts of congruent triangles; (19.0) Students use trigonometric functions to solve for
an unknown length of a side of a right triangle, given an angle and a length of a side.
Career and Technical Ed. Standards: (3.0) Career Planning and Management: Understand the scope of
career opportunities and know the requirements for educational training and licensure. Engineering Tech.
Pathway (B1.4) Apply conventional engineering measurement processes accurately (eg. laser transit, laser
levels, GPS instruments) for surveying and plan development.
Supplies/Set-up/Handouts: What is necessary for someone else to duplicate what you did?
(Include examples of all handouts, worksheets and transparencies)
Activity #1: Supplies needed for each pair of students: measuring tape, small mirror, calculator(optional),
handout and worksheets labeled: “Indirect Measurement Using Mirrors”.
Activity #2: Supplies needed for each pair of students: protractor, straw, string, paper clip, calculator or
trigonometric tables, handout and worksheets labeled: “Indirect Measurement Using a Clinometer”.
Evaluation Strategies
Students submit a poster with all calculations and drawings. The poster will be evaluated based on accuracy
of calculations, explanation of measurement differences, diagrams. Students will be given the following
instructions:
EVALUATION:
Your poster should be neat. Presentation is worth 15 points.
Your poster should address the following questions (25 points):
1. How is the angle reading from the clinometer related to the angle of elevation from
your eye to the top of the object you are measuring?
2. Draw and label a diagram showing the object and the measurements you made. Then
use trigonometric ratios to find the height of the object.
3. Repeat the activity, measuring the angle of elevation to the object from a different
distance. How does your result compare to the previous one?
4. Describe possible measurement errors that can be made in the activity.
5. Explain why this method of indirect measurement is useful in real-world situations.
ACTIVITY: INDIRECT MEASUREMENT USING A CLINOMETER
DETAILED INSTRUCTIONS FOR MAKING A CLINOMETER
A clinometer is a surveying tool that is used to measure angles of elevation and angles of
depression. Students can make a simple clinometer and use it to find the heights of tall objects
such as a flagpole or tree.
SUPPLIES:
Protractor
String
Straw
Paper clip
PROCEDURE:
First, tie a paper clip to the end of a 6-inch string. Second, tape the string’s other end to the
midpoint of the straight edge of a protractor. Third, tape a straw along the straight edge of
the protractor.
DETAILED INSTRUCTIONS FOR USING A CLINOMETER
First, identify the object you want to measure. Hold the clinometer steady and look through
the straw to sight the top of the object you are measuring. When the string stops moving,
pinch it against the protractor and record the acute angle measure.
PROJECT:
Create a poster (you decide the dimensions) which clearly shows how to use a clinometer to
measure angles of elevation and trigonometry to estimate the heights of objects.
EVALUATION:
Your poster should be neat. Presentation is worth 15 points.
Your poster should address the following questions (25 points):
6. How is the angle reading from the clinometer related to the angle of elevation from your
eye to the top of the object you are measuring?
7. Draw and label a diagram showing the object and the measurements you made. Then use
trigonometric ratios to find the height of the object.
8. Repeat the activity, measuring the angle of elevation to the object from a different
distance. How does your result compare to the previous one?
9. Describe possible measurement errors that can be made in the activity.
10. Explain why this method of indirect measurement is useful in real-world situations.