Teacher Notes



Teacher Notes
Publication No. 12532
Reaching New Heights with TriangulationStudent Laboratory KitMaterials Included In Kit
Protractors, 15
Rocket Image master Straw, clear, 15 String, 75 g Tape, cellophane, roll Washers, ¾", 15 Prelab PreparationPlace the Rocket Image high on the wall or prepare model rockets per manufacturer’s instructions. Safety PrecautionsStudents should not stare directly at the sun and should wear safety glasses to avoid contacting the straw with their eyes. Remind students to wash their hands thoroughly with soap and water before leaving the laboratory. DisposalAll materials in this kit may be reused. Lab Hints
Teacher Tips
Correlation to Next Generation Science Standards (NGSS)^{†}Science & Engineering PracticesAnalyzing and interpreting dataDisciplinary Core IdeasMSESS1.B: Earth and the Solar SystemHSESS1.B: Earth and the Solar System Crosscutting ConceptsScale, proportion, and quantityPerformance ExpectationsMSESS13. Analyze and interpret data to determine scale properties of objects in the solar system. Sample Data{12532_Answers_Table_1}
{12532_Answers_Figure_4}
To calculate the height of the object from the observer’s eye, use the following trigonometric formula:
Tan θ = opposite side/adjacent side {12532_Answers_Table_2}
Answers to Questions
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Student Pages


Student PagesReaching New Heights with TriangulationIntroductionFocus on making metric measurements through triangulation—an indirect means used for measuring the length of large or distant objects. Discover the height of a rocket using a protractor and some simple mathematics! Concepts
BackgroundTriangulation, which is used for many purposes including surveying and navigation, is the process of finding the distance to a point or the height of an object by calculating the length of one side of a triangle given the measurement of angles and sides (see Figure 1). A triangle is a closed geometric object composed of three straight line segments (threesided polygon). The angles of a triangle add up to 180°. There are three classifications of triangles based on the length of the sides and four based on the measure of angles. A scalene triangle is one in which there are no sides with the same (congruent) length, an isosceles triangle has two sides of the same length, and an equilateral triangle has all three sides the same length. An acute triangle is one in which each angle is less than 90°, a right triangle has one angle that measures exactly 90°, an obtuse triangle has one angle that measures more than 90°, and an equiangular triangle has all angles equal to 60°. The equilateral triangle and the equiangular triangle are the same. {12532_Background_Figure_1}
The position of celestial bodies such as stars and planets may be found using angles measured with an astrolabe, a historical astronomical instrument used to measure celestial angles. An improvement on the astrolabe was the sextant, which was used to measure the elevation of a celestial object from the horizon. The scale of the sextant is 1⁄6 of a circle (60°), the scale of the smaller octant is ⅛ of a circle (45°). Measuring objects on the Earth requires a different set of instruments. A theodolite is an instrument used in surveying, much like the sextant, to determine both horizontal and vertical angles. The transit is a simpler form of theodolite used in construction and often does not measure vertical angles. An altimeter is an instrument that will measure the height of an object based on changes in pressure. An alternative to using an altimeter is to use a simple altitude finder and, through triangulation, use angles to determine the height of an object. Experiment OverviewAssemble and use an altitude finder to triangulate the height of a rocket. Materials
Meter stick or metric tape measure
Protractor Rocket Straw, clear String, 12" Tape, cellophane Washer, ¾" Safety PrecautionsThe materials in this laboratory are considered nonhazardous, please observe normal laboratory procedures. Do not look at the sun and be careful when sighting to avoid contact with the eye. Wear safety glasses. ProcedurePreparation
Experiment
Student Worksheet PDF 