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SIGHTING ANGULAR SIZE
Elementary/Middle School (Grades 4-6)
Skill: Measurement (angle, length)
Specific Objectives:
- Construct a simple instrument (a quadrant) for measuring angular size.
- Observe how the angular size of an object depends upon its distance.
- Learn how angular measurements are used to find heights and distances.
Value
The students will gain an understanding of angular measurement and how it is used
for things such as surveying and astronomy.
The students will also develop an appreciation for the technology used in creating
ancient and modern scientific instruments.
Initial Learning Activity
Tell the students that the following activities will demonstrate how ancient astronomers made observations of the universe. Discuss the tools available to ancient astronomers
and the kinds of astronomical observations they might have made. You may want to have them research or just talk about astronomers such as Erastothenes, Ptolemy,
Copernicus and Galileo.
Materials
- 2 Bamboo Skewers
- lightweight posterboard or tagboard
- glue
- tape
- paperclip
PROCEDURE
A. Object of a known height within the classroom.
- Assemble the sighting instrument (see Attachment 3)
- Specify object to be measured inside the classroom (e.g. chalkboard, window)
and measure its height.
- Measure and label marks that are 3 and 5 meters away from the sighting object. You can also use marks 10 and 20 feet away from the object.
- Allow each student pair or group to stand at the 3 meter (or 10 foot) mark and
use the sighting instrument to find the angular size of the object. Repeat this
observation from the 5 meter (or 20 foot) mark.
Suggested Independent Follow-up Questions
- Ask what happened to the size of the sighting object and the measure of the angle
when the students moved back from 3 meters to 5 meters.
Answer: Size of the sighting object and angular size both decreased because when
you view an object from farther away it appears smaller, therefore its angular
size is smaller.
- Ask students to give examples of similar occurrences.
Answer: Plane viewed on the ground then in the air; boat seen in port then out
at sea.
- Ask the students to check the accuracy of their measurements:
a. For each sighting divide the height of the sighting object by the distance from
which the object was viewed to get the tangent of the angle.
b. Locate the tangent found in a. on Attachment 2 chart and identify the corresponding
angle measure.
c. Find the difference between your sighting angle measurements and Attachment
2 angle measurements. How close were your answers?
B. Object of unknown height.
- Select an object of unknown height such as a tree, building or telephone pole.
- Allow each student pair to measure the angular size of the object with their
quadrant.
- Use the tangent table (Attachment 2) to find the tangent of the measured angle.
- Use the formula: distance x tangent =height to find the height of the object.
DISCUSSION
- Discuss how angular measurements can be used to find the height of an object,
such as a mountain, that cannot be measured directly.
- Discuss how angular measurements can be used in astronomy to measure:
- Diameter of Moon or planet.
- Height of mountain on the Moon from their shadow length.
- Distance to a star from the parallax angle (Attachment 4).
Note:
The distance to the Moon is measured today by timing radar pulses reflected from
the Moon's surface.
+ Return to Lesson Plan List
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