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	Angle article - Angle rays endpoint vertex gradient geometry trigonometry Measuring - What-Means.com (Site not responding. Last check: 2007-10-08)
		Angles provide a means of expressing the difference in gradient between two rays meeting at a vertex without the need to explicitly define the gradients of the two rays.
		The degree measure of the angle is the length of the arc, divided by the circumference of the circle, and multiplied by 360.
		The symbol for degrees is a small superscript circle, as in 360°.
	www.what-means.com /encyclopedia/Angle (821 words)

	Angle - Wikipedia, the free encyclopedia
		Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays.
		The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection.
		This angle is equal to π/2 radians minus the angle between the intersecting line and the line that goes through the point of intersection and is perpendicular to the plane.
	en.wikipedia.org /wiki/Angle (1429 words)

	Small-angle formula - Wikipedia, the free encyclopedia
		The small-angle formula is a mathematical approximation, used in astronomy.
		It relates the linear size (D) of an object to its angular size (α) and its distance from the observer (d) and is a valid approximation if α is small.
		The number 206,265 is approximately equal to the number of arcseconds in a circle (1,296,000), divided by 2π.
	en.wikipedia.org /wiki/Small-angle_formula (110 words)

	Small-angle formula -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The small-angle formula is a (Click link for more info and facts about mathematical) mathematical approximation, used in (The branch of physics that studies celestial bodies and the universe as a whole) astronomy.
		It relates the linear size (D) of an object to its (Click link for more info and facts about angular) angular size (α) and its distance from the observer (d) and is a valid approximation if α is small.
		Here, α has to be measured in (A 60th part of a minute of arc) arcseconds.
	www.absoluteastronomy.com /encyclopedia/s/sm/small-angle_formula.htm (122 words)

	Ast 110: Class 9
		Small angle formula (repeat) --- we started talking about this by imagining an object at distance d that has an angular size a.
		I went on to show some examples of using this small angle formaula, the first one being to define a new unit of distance, the parsec, which is defined by using the observed property of parallax.
		In terms of the small angle formula, 1 parsec = 1 AU / 1 arc second (expressed in radians).
	www.ifa.hawaii.edu /~acowie/class99/class_9.html (939 words)

	Read about Grade (geography) at WorldVillage Encyclopedia. Research Grade (geography) and learn about Grade (geography) ... (Site not responding. Last check: 2007-10-08)
		Small-angle formula.) The ambiguities and the small differences that result may permit these two inconsistent approaches to coexist unrecognized, especially where all grades considered are subject to engineering upper limits of 15% or less.
		Expressing it as the angle from horizontal carries the same information, but may lead to confusion for readers who are not proficient in trigonometry.
		For instance, on hearing the same ground described as having 50% grade and also having 30 degrees inclination, one might falsely infer that a 5:3 ratio exists between the grade and the angle of inclination.
	encyclopedia.worldvillage.com /s/b/Grade_(geography) (303 words)

	ipedia.com: Angle Article (Site not responding. Last check: 2007-10-08)
		For other articles, see Angle An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.
		This angle is equal to π/2 minus the angle between the intersecting line and the line that goes through the point of intersection and is perpendicular to the plane.
		The obsolete format of angle used to indicate longitude or latitude is hemisphere degree minute' second", where there are 60 minutes in a degree and 60 seconds in a minute, for instance N 51 23′26″ or '''E 090 58′57″
	www.ipedia.com /angle.html (824 words)

	Basic Geometry
		For example, when the angle is small (say less than 25), the triangle below looks an awful lot like the wedge from the circle above.
		For this triangle, it is a good approximation to say that s, r, and are all related the small angle formula.
		In astronomy we are often working with very small angles, measured in arcseconds.
	boojum.as.arizona.edu /~jill/NS102_2004/geom.html (893 words)

	The Wall Sided Formula: Basics (Site not responding. Last check: 2007-10-08)
		The small angle approximation takes into consideration only the horizontal shift of the center of buoyancy during a heel angle.
		Since the vertical shift of the center of buoyancy is upwards, the wall sided formula produces a higher value for the righting arm than the small angle approximation.
		This assumption begins to break down as the angle phi is increased, especially close to the bow and the stern.
	web.nps.navy.mil /~me/tsse/NavArchWeb/1/module9/basics.htm (282 words)

	Student Worksheet 2
		The small angle approximation states: For small enough angles, the tangent of an angle is equal to the angle itself (when measured in radians).
		The entire angle is 10°, and it should be bisected by a dark line running along it that measures a smaller 5° angle.
		Use the small angle formula to determine the maximum distance (in light years) at which you could see this disk as more than a dot with your naked eye.
	www-glast.sonoma.edu /teachers/agn/studwk2.html (1506 words)

	USE OF THE SMALL ANGLE FORMULA (Site not responding. Last check: 2007-10-08)
		In astronomy the small angle relationship is used to find how far away a remote object is, by knowing its parallax angle using a baseline.
		The units of the number 57.3 are degrees, but the parallax angle is in arc seconds.
		Solving for the diameter, the small angle formula applied to this problem is:
	www.merritt.edu /~phys/example_problems.html (627 words)

	Astronomy 10: Parallax (Site not responding. Last check: 2007-10-08)
		This is a formula that describes the relationship between size, angular size, and distance.
		The exact formula involves trigonometry, but because we will be measuring small angles, we will manage just fine with this approximate formula.
		Protractors are fine for measuring large angles, but we need something better for measuring small angles.
	cse.ssl.berkeley.edu /bmendez/ay10/2002/projects/parallax.html (1140 words)

	Exams and Quizzes (Site not responding. Last check: 2007-10-08)
		Astronomers use the small angle formula and their measurement of the parallax angle to calculate distance to a star.
		Angular diameter is measured in __________ and represents the parallax angle.
		By astronomers agreement, the distance has units of _______________ as long as the linear diameter is in units of AU and the angle is measured in seconds of arc.
	www.harpercollege.edu /tm-ps/ast/101/exam.htm (695 words)

	Triangles & Small Angle Approximation (Site not responding. Last check: 2007-10-08)
		You are probably begining to realize that angles play an important part in astronomy.
		Because we shall be using the properties of triangles to help us work with angles, particularly very small angles.
		If you multiply the size of all 3 sides of a triangle by the same factor, then the angles remain the same.
	dosxx.colorado.edu /~bagenal/1010/Triangles.html (188 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Focal length of a lens Assuming a very thin lens and the small angle formula, derive an expression for the focal length of a lens whose surfaces have radii R1 and R2.
		Ellipses -Derive the formula for an ellipse in polar coordinates centred on one focus.
		Starting with this or the formula in Cartesian coordinates, show that the sum of distances from the two foci to any point on an ellipse is just 2a.
	astrowww.phys.uvic.ca /~pritchet/Astr200A/DeepThought.html (324 words)

	Small-Angle Formula (Site not responding. Last check: 2007-10-08)
		This is an extremely useful formula which is never directly stated in the text.
		Basically this formula relates the angular size of an object
		(it is a good idea to always convert angles to arc seconds before beginning) and d = 20 cm.
	ceres.hsc.edu /homepages/classes/astronomy/fall97/Mathematics/sec9.html (185 words)

	Encyclopedia article on Angle [EncycloZine] (Site not responding. Last check: 2007-10-08)
		The difference between an acute angle and a right angle is termed the complement of the angle, and between an angle and two right angles the supplement of the angle.
		If a straight line intersects two [[Parallel (geometry) parallel]] lines, corresponding angles at the two points of intersection are equal; adjacent angles are complementary, that is they add to π radians or 180°.
		Constructing a triangle from its angle bisectors (http://www.cut-the-knot.org/triangle/TriangleFromBisectors.shtml)
	encyclozine.com /Angle (1209 words)

	Re: [RCSE] calculating height using small angle formula
		The angle that should come from the above is: angle = 360º/552.64 = 0.6515 degrees That is, you had the angle calculation inverted.
		:-)) Using the equation that you listed, the distance is: R = 100" / 0.6515 º x 57.3 = 3732" = 733 ft Alternately, you don't have to solve for the angle at all.
		Re: [RCSE] calculating height using small angle formula Joe and Jan Wurts
	www.mail-archive.com /joewurts@csi.com/msg00018.html (213 words)

	Implication 1 (Site not responding. Last check: 2007-10-08)
		Because the parallax angle p is always extremely small, a simple formula connects it to the distance d between a star and our Sun:
		A parsec is defined to be the distance from our Sun to a star that shows a parallax angle of one second of arc when Earth's orbit is used as a baseline.
		Another common unit for measuring stellar distances is the light-year, the distance light travels in a year.
	www.people.vcu.edu /~rgowdy/astro/mod/043/t3/imp.html (73 words)

	Greek Astronomy II (Site not responding. Last check: 2007-10-08)
		When objects subtend less than about 10 degrees of arc we can use the approximation (to quite good accuracy) that the trigonmetric functions of tan and sin can be considered equal to the angle itself (in a unit called radians rather than degrees).
		Call the distance to the object D. This is again considering small angles (less than ten degrees).
		Given the distance to the Moon we could reverse the previous process and use the small angle equation to get the linear size of the Moon and then the distance to and size of the Sun.
	www.astro.queensu.ca /~waugh/fallterm/qlecture6.html (777 words)

	Determining the distances to objects in the Universe (Site not responding. Last check: 2007-10-08)
		Once you know the size of something, you can determine how far away it is pretty easily by measuring the angular size of the object.
		The angular size of an object is determined by its actual size and how far away it is. Figure 3 shows this relationship, along with the small angle formula astronomers use to measure distances to objects with known sizes.
		Figure 5: Measuring the parallax angle (and the distance!) of a star.
	aeon.physics.weber.edu /jca/PHSX1030/LectureNotes/Lecture_15/node1.html (448 words)

	Ch. 6 Solutions - PHYS130, Dr. Giblin (Site not responding. Last check: 2007-10-08)
		If we know the distance, then we can apply the small angle formula to obtain the actual size of the smallesst discernable feature.
		(Recall the small-angle formula from our review at the beginning of the semester.) From Figure 6-31, we see that the distance to the galaxy is d=70 million light years.
		That is, it takes 70 million years for the light from the galaxy to reach the Hubble Space Telescope.
	www.cofc.edu /~giblint/ch6soln_fk.html (393 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		I will use the small angle formula for arc-seconds and then convert to arcminutes.
		If two dark lines on an eyechart are 2 mm apart, how far away can the person be and still see the lines as distinct?
		Solution : also use the small angle formula.
	www.phys.lsu.edu /faculty/cjohnson/soln2.html (208 words)

	NASA CSU SASS - Program Descriptions - 2003 - 2004
		Learn about the small angle formula; take notes for future reference.
		Calculate the changing distance to Mars as Earth and Mars move in their orbits.
		By using HOU-IP software tool, slice to find the diameter in pixels; calculate the angular size of the images; look up the actual diameter of Mars in kilometers; and then use the small angle formula to calculate the distance to Mars.
	hou.lbl.gov /~vhoette/Explorations/sass/index2003fall.html (929 words)

	Answer 3. Angular Size Of The Sun (Site not responding. Last check: 2007-10-08)
		Using the small-angle formula, you can work out the Sun's true angular size from its distance and diameter, which are given in the book:
		The answer is no, just so long as you use the same units for d and L in the small-angle formula!
		When you use the same units, d÷L is a pure number, with no units attached.
	www.ifa.hawaii.edu /faculty/barnes/ast110_99/homework/ans3.html (182 words)

	Prof. L. Sparke Astronomy 100 Name_______________
		Formulas: these will be given on the exam.
		You don't need to memorize them, but make sure you understand them.
		As seen from the Moon, the Earth covers an angle on the sky of
	www.astro.wisc.edu /~sparke/F00_A103_6-wk_review.html (548 words)

	Lecture 3 (Site not responding. Last check: 2007-10-08)
		Reverse of small angle formula-- use parallax to measure distances (e.g., surveyors)
		Distance from your face to your finger: parallax is 5
		Formula for the volume of a sphere: V = (4/3)
	www.phys.lsu.edu /faculty/cjohnson/lecture3.html (302 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations (Site not responding. Last check: 2007-10-08)
		Energy Citations Database (ECD) Document #4214878 - A look at the small-angle end of the Rutherford scattering formula
		Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
		A look at the small-angle end of the Rutherford scattering formula
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=4214878 (105 words)

	First Discoveries/Copernican Revolution
		For more on the small angle formula go here.
		Difference in length of shadows related to the angle at which you are looking at Sun
		divide the difference by two to get the angle of the tilt
	ngala.as.arizona.edu /nats102/lecture4.html (255 words)

	Lecture 7 - Angular Diameter and Lunar Eclipses (1/29/96) (Site not responding. Last check: 2007-10-08)
		Refraction of Sunlight in Earth's atmosphere: red moon at totality
		The Small Angle Formula: Arc of a Circle
		The Aberration of Starlight and the Earth's Motion
	www.aoc.nrao.edu /~smyers/courses/astro01/L7.html (396 words)

	Physics 181 -- Astronomy (Site not responding. Last check: 2007-10-08)
		Eclipses: when can we see them, why don't we always see them
		Angles in a circle and the small angle formula
		alpha = 206265 D/d - small angle formula
	einstein.drexel.edu /~hoyle/summery.html (275 words)

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