To approximate the distance from the Earth to stars relatively close by, astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with

Algebra and Trigonometry (MindTap Course List)
4th Edition
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Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter7: Analytic Trigonometry
Section7.4: Basic Trigonometric Equations
Problem 1E: Because the trigonometry functions are periodic, if a basic trigonometric equation has one solution,...
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To approximate the distance from the Earth to stars relatively close by, astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's
point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is
at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with <PSE = 90°. The length of is the distance between the Earth and Sun, approximately 92,900,000
mi. The parallax angle (or simply parallax) is denoted by p. Use this information for Exercises 31-32.
Earth
Sun
Star
Parallax angle
Earth
Background stars
Transcribed Image Text:To approximate the distance from the Earth to stars relatively close by, astronomers often use the method of parallax. Parallax is the apparent displacement of an object caused by a change in the observer's point of view. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers measure a star's position at times exactly 6 months apart when the Earth is at opposite points in its orbit around the Sun. The Sun, Earth, and star form the vertices of a right triangle with <PSE = 90°. The length of is the distance between the Earth and Sun, approximately 92,900,000 mi. The parallax angle (or simply parallax) is denoted by p. Use this information for Exercises 31-32. Earth Sun Star Parallax angle Earth Background stars
32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles.
b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint: 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 1012 mi.)
Transcribed Image Text:32. a. Find the distance between the Earth and Barnard's Star if the parallax angle is 0.547 arcseconds. Round to the nearest hundred billion miles. b. Write the distance in part (a) in light-years. Round to 1 decimal place. (Hint: 1 light-year is the distance that light travels in 1 yr and is approximately 5.878 × 1012 mi.)
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