


Mathematics Skill or Topic Area: Applications of Angular Measure 

Next Gen Science Standards: PS3: Energy; ETS 1: Engineering Design Common Core ELA for Science: RST.68.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions; RST.68.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.68.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic. Common Core Math Standard: CC.7.G.2 Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides. 

Video Engagement: Transits Discover how scientists used the last Venus transit and a geometric technique called parallax to verify the distance between the sun and Earth. Find out what scientists hope to learn the next time Venus transits the face of the sun in June 2012 (5 minutes). View Program 


Explore math connections with SpaceMath@NASA 

Problem I  Angular Size and Similar Triangles   A critical concept in astronomy is angular size, measured in degrees, minutes or arcseconds. This is a review of the basic properties of similar triangles for a fixed angle. Topics include geometry, similar triangles and proportions. [Open PDF] Problem II  The Last Total Solar EclipseEver!  Students explore the geometry required for a total solar eclipse, and estimate how many years into the future the last total solar eclipse will occur as the moon slowly recedes from Earth by 3 centimeters/year. Topics include angular measure and rates of change. [Open PDF] Explain your thinking: Write your own problem  Using information found in the Math Connection problems, the press release or the video program, create your own math problem that involves angle measure or parallax. Explain why you set the problem up this way, and how you might find its answer. Evaluate your understanding: Challenge Problem  Imagine looking down on a scale model of the solar system showing the concentric circular orbits of Venus and Earth with our sun at the center. On March 26, 2012 the angle between the Earth, Sun and Venus (ESV) measured 45 degrees. The angle between Venus, Earth and the Sun (VES) measured 46 degrees and the angle between Earth, Venus and the Sun (EVS) measured 89 degrees. As viewed in the evening sky from Earth, what will be the angular separation between Venus and the Sun at sunset? You might want to draw a scaled model to help you visualze the angles. Explain how you arrived at your answer. Answer: The relevant angle is VES which is 46 degrees. Astronomers call this the Greatest Eastern Elongation of Venus.


NASA / JPL 3D Solar System 

Extend your new knowledge  Students use the Eyes on the Solar System simulator to study the geometry of the transit of Venus, and use what they have learned to predict the transit for the year 2125. [ Open PDF ] 
