# Reaching New Heights with Triangulation

## Student Laboratory Kit

### Materials Included In Kit

Protractors, 15
Rocket Image master
Straw, clear, 15
String, 75 g
Tape, cellophane, roll
Washers, ¾", 15

### Prelab Preparation

Place the Rocket Image high on the wall or prepare model rockets per manufacturer’s instructions.

### Safety Precautions

Students 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.

### Disposal

All materials in this kit may be reused.

### Lab Hints

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. This laboratory activity can reasonably be completed in one 50-minute class period.
• As an alternative to using the Rocket Sheet, use the altitude finder to determine the height of model rockets.
• The height of a monster or other object could be determined. Be creative in devising a scenario.
• Have students sight helium balloons as they ascend after they are released. To steady and slow the ascent, tie a washer to the balloon.
• Use the altitude finder to determine the height of a flagpole, building, house, tree, chimney, etc.

### Teacher Tips

• Use this activity to teach students that not all measurements are direct.
• Coordinate with the math teacher to teach about angles, trigonometry and geometry.

### Science & Engineering Practices

Analyzing and interpreting data

### Disciplinary Core Ideas

MS-ESS1.B: Earth and the Solar System
HS-ESS1.B: Earth and the Solar System

### Crosscutting Concepts

Scale, proportion, and quantity

### Performance Expectations

MS-ESS1-3. Analyze and interpret data to determine scale properties of objects in the solar system.

### Sample Data

To calculate the height of the object from the observer’s eye, use the following trigonometric formula:

Tan θ = opposite side/adjacent side
Opposite side (height of object from eye) = tan θ x adjacent

1. Triangles are named based on what two measurements?

Triangles are named based on the lengths of the sides or the sizes of the angles.

2. What type of triangle was used in this activity?

A right triangle was used to determine the height of the rocket.

3. Why is it important to know the height of the eye?

It is important to know the height of the eye because that quantity added to the height of the rocket from the eye gives the total altitude of the rocket.

4. The rocket image is that of the Saturn V, used to send Apollo to the Moon. The image is 24 cm tall. The actual Saturn V rocket is 110.64 m tall. Determine the scale of the rocket and use the scale to determine the height of the rocket if were actually a Saturn V being launched.

The scale of the rocket is 461:1 (110.64 m / 0.24 m = 461). Student answers will vary based on the height of his rocket. Using the sample data, the rocket would be at an altitude of 1153 m (2.5 m x 461 = 1153 m).

# Reaching New Heights with Triangulation

### Introduction

Focus 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

• Indirect measurement
• Triangulation

### Background

Triangulation, 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 (three-sided 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  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 Overview

Assemble 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 Precautions

The 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.

### Procedure

Preparation

1. Lay the straw over the protractor so that the straw crosses the 90° mark as shown in Figure 2.
{12532_Procedure_Figure_2}
2. Position the straw so that approximately one centimeter hangs over the flat end of the protractor.
3. Using cellophane tape, securely tape the straw to the protractor.
4. Cut a piece of string approximately 12 inches long.
5. Tie a washer onto one end of the string.
6. Tape the other end of the string to the protractor next to the straw as shown in Figure 3. Note: The string should be free to hang down to the 0° mark when the straw is held horizontal to the ground.
{12532_Procedure_Figure_3}

Experiment

1. Hold the altitude finder so that the weighted string hangs freely. Note: The string should hang down past the 0° mark when the straw is parallel to the ground.
2. Look through the straw (sight) and position the altitude finder so that the top of the rocket is visible through the straw as seen in Figure 4 in the worksheet.
3. Once the top of the object has been sighted, record the elevation angle (degree mark through which the string passes) on the Reaching New Heights with Triangulation Worksheet. Note: This angle will be between 0° and 90° and is referred to as angle theta (θ).
4. Using a meter stick or metric tape measure, measure the horizontal distance between the observer and the point from which the rocket left the ground. For an actual rocket this would be the launch pad and for an image of a rocket on the wall it would be the base of the wall.
5. Record the horizontal distance on the Reaching New Heights with Triangulation Worksheet. Note: This is the adjacent side of the triangle.
6. Using a meter stick, measure the height of the observer’s eye from the ground.
7. Record the height of the observer’s eye on the Reaching New Heights with Triangulation Worksheet.
8. Complete the calculations on the Reaching New Heights with Triangulation Worksheet to determine the height of the rocket.

### Student Worksheet PDF

12532_Student1.pdf

Next Generation Science Standards and NGSS are registered trademarks of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards were involved in the production of this product, and do not endorse it.