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Trigonometry Lesson Plan
Trigonometry via Mobile Devicei
Overview of
Lesson
Students investigate the relationships between angles and side lengths in right
triangles with the help of materials found in the classroom and a mobile device.
Using all or part of a meter stick or dowel and text books or other supplies,
students build right triangles and measure the angles using a clinometer
application on an Android® (phone or tablet) or iOS® device (iPhone® or
iPad®). Then they are challenged to create a triangle with a given side length
and one angle. The electronic device is used to measure the accuracy of their
constructions.
Description of
Learners
Intended
Learning
Goals
Grade 11 - Students should have a basic understanding of trigonometry and
know how to run an application on a mobile device.
Lesson
Content
Learning
Objectives
Students will explore the applications of trigonometry in a hand-on activity using
a smartphone (or tablet) application.




To understand the application of trigonometry in
engineering/architecture.
To understand how to use the clinometer app and how it can be used in
real-world engineering/architecture.
Using a clinometer app, students should be able to measure the angles in
right triangles.
Given a side and angle, students should be able to use trigonometry to
find the (length) sides of a triangle, correctly to one decimal point.
*All measurements should be accurately measured/calculated to one decimal point and in
centimeters (when applicable).
Standards
Common Core State Standards for Mathematics
 6. Understand that by similarity, side ratios in right triangles are properties
of the angles in the triangle, leading definitions of trigonometric ratios for
acute angles. (Grades 9-12) [2010]
 8. Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems. (Grades 9-12) [2010]
Materials
Each group needs:
 yard or meter stick (or tape measure)
 sticks or dowels of varying lengths
 5-6 textbooks or other stackable objects
 masking tape (to hold shapes forming the right triangle in place)
 Android device (phone or tablet) or iOS device (iPhone or iPad)
 clinometer app
 Post-Activity Quiz, one per student
Procedures
Introduction

Have you ever wondered how to calculate the height of a flagpole or a
tree fort or the building across the street? Have you ever wondered why
Engineering/Architecture Applications
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Trigonometry Lesson Plan

bridges or other structures remain standing?
o Part of the answers to these questions comes from the engineer's
application of trigonometry.
Civil engineers use trigonometry to help design many structures or to
troubleshoot problems. They also use trigonometry to calculate the forces
at work on objects so that they understand why something moves or does
not move.
Before the Activity
 Prepare the Android and/or iOS devices with a clinometer app.
 Gather the other materials. It is recommended that you provide a variety
of stick lengths, so groups are doing calculations different from other
groups. Be sure you know the length of each stick, that is, stick A = 8
inches, stick B = 11 inches, etc.)
 Make copies of the Post-Activity Quiz.
 Divide the class into groups of three students each.
With the Students
1. To begin, provide each group with a stick of a known length. NOTE: Give
each group a different length stick so that each has different calculations.
2. Provide each group with a length measuring tool and an Android or iOS
device with clinometer app installed.
3. Working in their groups, have students construct right triangles using their
stick as the hypotenuse and textbooks or other classroom supplies as the
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Trigonometry Lesson Plan
two legs (see Figure 1). Use tape to attach the stick to the book stack so
that it does not slip; alternatively, place a heavy object at the base of the
stick to keep it from slipping.
4. When you have a right triangle formed, use the mobile device and its
clinometer app to measure the angles of the triangle and explore the
relationships between the angle measures and the side lengths. The
Android or iPad must be nearly vertical to use the angle measuring
function of the clinometer. When the clinometer has 0° located at the top,
rotate the Android or iPad device left or right until the top or bottom of
the device matches the sloped side of the angle. The other side of the
angle should be horizontal. Then read the degree measure of the angle
from the clinometer. See Figure 2 for more information.
5. After some exploration and practice with the clinometer, inform the teams
that they will be given a specific triangle to construct. To accomplish this,
students must apply engineering design. Provide each group with a stick
of fixed length (this can be a yard or meter stick, or any stick-like object
found in the classroom), which represents the hypotenuse of a right
triangle. Tell students they can measure this object and use the recorded
length in their calculations.
6. Provide each group with a target angle. (NOTE: Assign each group a
different acute angle.) The challenge is to create a triangle that has the
stick as its hypotenuse and the given angle as one of the acute angles.
7. To begin, have students create a rough draft drawing and calculations of
their triangle designs.
8. After a firm plan has been developed, students create polished final drafts
of their proposals for the dimensions of the triangle. Require the final drafts
to include brief explanations of numerical results.
9. Using their final drafts as a guide, teams build their triangles using a stick
and textbooks, blocks, desks or any other teacher-approved classroom
objects.
10. Once a group has its right triangle constructed, have the teacher or
another student group verify the result using the clinometer app.
11. To conclude, have students write up an explanation of the design process
they went through to create their final products. Require the explanation
to include final drawing and calculations.
Assessment
Quiz: Administer the Post-Activity Quiz to assess students' understanding and
ability in applying trigonometric ratios to problems based on a real-life scenario—
calculating measurements related to building a radio tower.
References
Contributors: Scott Burns
Copyright: © 2014 by Regents of the University of Colorado; original © 2013
University of Nebraska
Adapted from https://www.teachengineering.org/view_activity.php?url=collection/uno_/activities/
uno_handheld/uno_handheld_lesson01_activity1.xml
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Engineering/Architecture Applications
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