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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 1 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 Engineering/Architecture Applications 2 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 i Engineering/Architecture Applications 3