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Topic: Acute angles

	Angle
		Mathematicians generally prefer angle measurements in radians because this removes the arbitrariness of the number 360 in the degree system and because the trigonometric functions can be developed into particularly simple Taylor series if their arguments are specified in radians.
		The angle of two intersecting curves is defined to be the angle between the tangents at the point of intersection.
		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.
	www.sciencedaily.com /encyclopedia/angle (809 words)

	Complementary angles -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		A pair of (The space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians) angles are complementary if the sum of their measures is 90 (A specific identifiable position in a continuum or series or especially in a process) degrees.
		If the two complementary angles are adjacent (i.e., have a common vertex and share a side, but do not have any interior points in common) their non-shared sides form a (The 90 degree angle between two perpendicular lines) right angle.
		An acute angle is filled up by its complement to form a right angle, which is the most basic kind of angle, because it can be constructed by drawing the angle bisector of a line.
	www.absoluteastronomy.com /encyclopedia/c/co/complementary_angles.htm (178 words)

	Angle - Wikipedia, the free encyclopedia
		Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other.
		In mathematics radians are assumed unless specified otherwise because this removes the arbitrariness of the number 360 in the degree system and because the trigonometric functions can be developed into particularly simple Taylor series if their arguments are specified in radians.
		If a straight transversal line intersects two parallel lines, corresponding (alternate) angles at the two points of intersection are equal; adjacent angles are supplementary, that is they add to π radians or 180°.
	en.wikipedia.org /wiki/Angle (1431 words)

	Angles and angle terms
		An acute angle is an angle measuring between 0 and 90 degrees.
		An obtuse angle is an angle measuring between 90 and 180 degrees.
		Angle B and angle C are also alternate exterior angles.
	www.mathleague.com /help/geometry/angles.htm (516 words)

	Teaching Angles (Site not responding. Last check: 2007-10-08)
		Gates and Griffin suggest that ‘describing an angle as a measure of pointedness is fine when an angle is acute, but if pupils are asked to consider an obtuse or reflex angle such representation may lead to errors’ (1988).
		For example describing a reflex angle of 300º as a ‘corner’ or a ‘point’ seems unhelpful and as Gates and Griffin point out ‘in the case of angle it seems common for pupils of all ages to confuse ‘angle’ with ‘arc’ and ‘vertex’’ (1988).
		Instead of correctly comparing the angles in each case students would have appeared to succeed by comparing the ‘distances across the open end of the angle’, the ‘triangular areas enclosed’, the ‘arc lengths’ or the ‘areas of sectors enclose by the arcs’.
	s13a.math.aca.mmu.ac.uk /Student_Writings/CDAE/AnnaJordan.html (7532 words)

	Apparatus for cross cutting coiled strip into rectangular and oblique angled plates and cutting off acute angles - ...
		After the acute angle has been cut off, the plates are removed in the transverse direction, which accounts for an increased length of the line under review.
		The non-pivoted shears 5, which are intended for cutting off the acute angles of plates, are mounted on a slider 9 which is arranged behind the pivoted shears 4 in the direction of the strip movement.
		In this latter case, the stip braking distance, which is measured, is greater than the distance between the transducer and the stop, the axes of the stops being spaced from the axle of the pivoted shears at a distance which is equal to a preselected plate length.
	freepatentsonline.com /4077287.html (5867 words)

	Topics in trigonometry: The definitions of the trigonometric functions (Site not responding. Last check: 2007-10-08)
		A right triangle is composed of a right angle, the angle at C, and two acute angles, which are angles less than a right angle.
		Each acute angle is formed by the hypotenuse and the side adjacent to the angle.
		Let x be the segment of the base containing the angle A. Then the remaining segment is the difference between the whole c and that segment: c − x.
	www.themathpage.com /aTrig/definitions-trigonometric.htm (637 words)

	ez1-6 Exploring Angles (Glencoe Geometry) (Site not responding. Last check: 2007-10-08)
		- An angle separates a plane into THREE distinct regions, the interior of the angle, the exterior of the angle, and the angle itself.
		acute angles are always less than 90 degrees.
		Equal measure angles are labeled as shown in the diagram.
	www.e-zgeometry.com /class/class1/1.6/1.6.htm (527 words)

	Ink jet printhead wiper having side surfaces intersecting a top surface at acute angles to form wiping edges and a slat ... (Site not responding. Last check: 2007-10-08)
		That is, the angles between surface 82 and surface 84, and surface 82 and surface 86 are acute angles.
		The angles should be as small as possible consonant with the material used and the limitations of the process for molding the material.
		9, because of the acute angle formed between surfaces 82 and 84, rather than a right angle as exists between surfaces 94 and 93, the angle between surfaces 102 and 84 is greater than the angle between surfaces 102 and 93.
	www.freepatentsonline.com /5612722.html (3880 words)

	Trigonometric Functions of Acute Angles (Site not responding. Last check: 2007-10-08)
		In general, the sine of an acute angle is equal to the cosine of the complement of that angle.
		Similarly, the tangent of an angle is equal to the cotangent of its complement and the secant of an angle is equal to the cosecant of its complement.
		You calmly estimate the angle of elevation to Gigantor's mouth to be 70°.
	www.lhs.logan.k12.ut.us /~rweeks/trig/rightangletrig.htm (1017 words)

	Fun With Right, Acute, and Obtuse Angles (Site not responding. Last check: 2007-10-08)
		Draw a picture of the location of the acute angle you found and describe where the angle was found.
		One way to remember this angle is to say, "An acute angle is a cute little angle." The teacher should make an acute angle by bending his/her left arm at the elbow and holding the arm across the chest pointing toward the right shoulder.
		Confirm that it is an acute angle and ask them if they think an acute angle measures more or less than 90 degrees and ask them to give a reason for their response.
	www.richlandclicks.org /Teacher/connections/grade4/funwithangles.htm (2049 words)

	Trigonometric Functions (Site not responding. Last check: 2007-10-08)
		The ancient Greek geometers only considered angles between 0° and 180°, and they considered neither the straight angle of 180° nor the degenerate angle of 0° to be angles.
		We use the coordinates of B to define the cosine of the angle and the sine of the angle.
		Specifically, the x-coordinate of B is the cosine of the angle, and the y-coordinate of B is the sine of the angle.
	aleph0.clarku.edu /~djoyce/java/trig/functions.html (1368 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-08)
		Therefore if the sum of any set of exterior angles exceeds 360 degrees, the sum of all the exterior angles must be even greater; but this can't be.
		The exterior angle is the supplement of the corresponding interior angle, that is, 180 degrees minus the interior angle.
		The number you find this way is the same as the number of acute angles in the example that Dr. Douglas found, so we know that this number of acute angles is possible -- it is the greatest possible.
	mathforum.org /library/drmath/view/60783.html (729 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-08)
		If one angle of a triangle is obtuse (bigger than a right angle), then the others both have to be acute (less than a right angle).
		You can either see that by just drawing an obtuse angle and seeing what happens if you make a second angle obtuse, or by knowing that the sum of the angles is always 180 degrees.
		This means that you have to have at least two acute angles.
	mathforum.org /library/drmath/view/55061.html (254 words)

	Illustration of proper mathematics proof and solution
		The first assertion follows from the second assertion and the fact that the exterior angle at a vertex is supplementary to the internal angle of the polygon at the vertex.
		Suppose the number of acute angles in the polygon is at least 4.
		To complete the proof that the maximum number of acute angles is three, we need to prove that, for any n, there is a convex n-gon with three acute angles.
	www.mathpath.org /MathPath_Quiz_2003_files/example.htm (2260 words)

	Angles Discussion (Site not responding. Last check: 2007-10-08)
		An acute angle is an angle whose measure is less than 90 degrees.
		We are going to look at the angles formed when two parallel lines are intersected by a third line called a transversal.
		Mentor: Yes, alternate interior angles are angles that are inside the parallel lines and on opposite sides of the transversal.
	www.shodor.org /interactivate/discussions/angles.html (542 words)

	Angles and Polgons: Mathematics 10 (Site not responding. Last check: 2007-10-08)
		Since all the interior angles of a regular polygon are equal and all the exterior angles of a regular polygon are equals.
		To determine the measure of an angle given the value of one trigonometric ratio of the angle by using the calculator or tables.
		The students may require practice in labeling the right angle, triangles in terms of hypotenuse, side adjacent and side opposite with reference to one of the two acute angles.
	142.3.219.38 /RR/database/RR.09.96/seidler1.html (1665 words)

	Acute and Obtuse Angles
		Point out that the angle is a quarter turn regardless of the length of the arms.
		Introduce the term acute angle as being an angle less than a right angle.
		The teacher should move around the classroom and ask students questions to determine their progress, such as, what type of angle is being produced by the hands on the clock on the wall.
	hrsbstaff.ednet.ns.ca /davilynw/WebGems/Lesson%20Plans/Geometryplans/Acute%20and%20Obtuse%20Angles.htm (531 words)

	Angles Math Lesson Plan, Thematic Unit, Activity, Worksheet, or Mathematics Teaching Idea
		Be sure to instruct them on what angles they are forming (right, obtuse or acute) and how to properly form the angles.
		Stress that all of the square’s angles are right angles equal to 90oeach, and that some geometric shapes will have right angles, but that all of the angles may not be right angles.
		Once the angles are properly formed, the students should glues the angles to the tag board, clearly label the angles, and provide a definition of the angles underneath.
	www.lessonplanspage.com /MathRightAcuteObtuseAngles6.htm (462 words)

	Mathematics TEKS Toolkit (Site not responding. Last check: 2007-10-08)
		Students construct an angle maker by joining two cardboard strips with a brass fastener and use it to replicate angles found on real objects, such as the hands on an analog clock at a specific time, the corner of a room, or an open pair of scissors.
		They compare the right angles to other angles, such as where a brace is fastened onto a desk or the hands of an analog clock at a certain time.
		Students predict whether the angle they have located has a measure greater than a right angle (obtuse), less than a right angle (acute), or about the same as a right angle, then use their model of a right angle to test their predictions.
	www.tenet.edu /teks/math/clarifying/assessconn43.html (1945 words)

	[No title]
		Then subdivide each of the two triangles into 10 smaller ones, by adding a small triangle in the middle (each of whose corners connects to one of the outer triangle), and adding one point on each side of the outer triangle, connecting to two corners of the inner one.
		The problem is I'm not sure which angles should up being equal when w,x,y are chosen so as to minimize the largest angle...
		By fixing some angles and optimizing a remaining single parameter I found a solution with all angles smaller than 84 degrees, but it seems something close to 80 degrees should be feasible.
	www.math.niu.edu /~rusin/known-math/96/acute.tri (945 words)

	Acute Square Triangulation
		An old puzzle asks for a partition of the square into triangles in which all angles are strictly acute.
		One of the ideas in that paper was to define certain "tiles" that could be placed on the squares of a quadtree, to form acute-angled triangulations.
		Returning to Tromp's question on achieving better angles, a result of Gerver implied that the square could be partitioned into 72-degree triangles, not necessarily meeting edge-to-edge.
	www.ics.uci.edu /~eppstein/junkyard/acute-square (586 words)

	Math B
		An acute angle is an angle whose measure is greater than 0° and less than 90º.
		An angle bisector is a ray whose endpoint is the vertex of the angle and which divides the angle into two congruent angles.
		The sum of the measures of the angles in a linear pair is 180º.
	regentsprep.org /Regents/mathb/1A/vocab.htm (405 words)

	Reversing a GDSII file - Convertion to PG
		There are also some special settings we'll use to reduce the number of acute angles in the drawing and avoid small geometries that are less than the minimum flash size that the PG machine can handle.
		The reason we want to avoid acute angles is because the Pattern Generators can only image rectangles so there is always going to be a small approximation when dealing with acute angles.
		However, such angles which are less than 90 degrees should be avoided, especially in narrow traces where a margin of error could have a significant effect on the circuit.
	www.artwork.com /polygon/faq/acute.htm (643 words)

	ez 4-1 Classifying Triangles (Glencoe Geometry) (Site not responding. Last check: 2007-10-08)
		All triangles have at least two acute angles, but the third angle, which is used to classify the triangle, can be acute, right, or obtuse.
		triangle is an acute triangle in which all angles are congruent.
		The two angles formed by the base and one of the legs are called
	www.e-zgeometry.com /class/class4/4.1/4.1.htm (311 words)

	The 3 types of angles Math Lesson Plan, Thematic Unit, Activity, Worksheet, or Mathematics Teaching Idea
		As I call out an angle, the students will take their arms and form that type of angle; ex.
		Day 3-----TLW be given pictures of different geometric figures and name cards (parallel lines, perpendicular lines, right angles, obtuse angles, acute angles, intersecting lines, etc.) The students will play a game of concentration with the cards, matching the picture with its correct name.
		TLW trace all the acute angles in red, all obtuse angles in blue, and all right angles in green.
	www.lessonplanspage.com /Math3TypesAngles56.htm (265 words)

	Lesson: Angles (Site not responding. Last check: 2007-10-08)
		It is also designed to introduce students to vertical angles, adjacent angles, alternate interior angles and alternate exterior angles.
		Open your browser to the angles activity in order to demonstrate it to the students.
		Print out a sample set of angles from the web site, and have that be the one students use to complete the worksheet.
	www.shodor.org /interactivate/lessons/angles.html (599 words)

	angles
		Exterior angles are angles on the outside of any shape.
		Vertical angles are 2 angles connected together at their vertex, with both of the angles sharing the two lines making them.
		are angles that are in the same position in relation to the lines they are positioned on.
	www.cobb.k12.ga.us /~smitha/ANGLES.html (394 words)

	Finding angles and lines in pictures (Site not responding. Last check: 2007-10-08)
		Identify four angles that use the chimney as one of its sides.
		Sketch the angles in the picture and circle the vertex.
		Describe the location of 4 acute angles, 1 right angle, 2 obtuse angles, 2 sets of parallel lines and 2 sets of perpendicular lines.
	leader.education.louisville.edu /edtl/thompson/edem629/sum01/anglesandlinestudent.htm (163 words)

	Management of patients with narrow angles and acute angle-closure glaucoma » Clinical and Experimental Optometry (Site not responding. Last check: 2007-10-08)
		Background: Acute closure of the anterior chamber angle can have catastrophic consequences for vision when it occurs in an unsupervised situation.
		Case report: We report on the case of a 59-year-old white female whose anterior chamber angles closed in response to mydriatic drops instilled during an optometric examination.
		Conclusion: We conclude that the optimal standard of care for patients presenting to an optometric practice, and who are subsequently found to have narrow anterior chamber angles, includes pupillary dilatation to allow stereoscopic visualisation of the optic nerve head.
	www.optometrists.asn.au /ceo/backissues/vol81/no6/973 (221 words)

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