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Topic: Right triangle

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In the News (Mon 22 Jul 19)

 AllRefer.com - triangle, in mathematics (Mathematics) - Encyclopedia
In Euclidean geometry the sum of the angles of a triangle is equal to two right angles (180°).
In geometry it is shown that two triangles are congruent (i.e., are the same shape and size) if, in general, any three independent parts (sides or angles) of one are the same as the corresponding three parts of the other.
The triangle is the simplest of the polygons (i.e., it has the least possible number of sides).
reference.allrefer.com /encyclopedia/T/triangl1.html   (399 words)

 Pythagorean theorem   (Site not responding. Last check: 2007-11-07)
The sum of the areas of the squaress on the legs of a right triangle is equal to the area of the square on the hypotenuse.
A right triangle is a triangle with one right angle; the legs are the two sides that make up the right angle, and the hypotenuse is the third side opposite the right angle.
If a tetrahedron has a right angle corner (a corner of a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.
www.sciencedaily.com /encyclopedia/pythagorean_theorem   (1061 words)

 Relations and sizes - Right triangle facts - In Depth   (Site not responding. Last check: 2007-11-07)
This version of the right triangle is so popular that plastic models of them are manufactured and used by architects, engineers, carpenters, and graphic artists in their design and construction work.
The ratio of this triangle's longest side to its shortest side is "two to one." That is, the longest side is twice as long as the shortest side.
He proved that, for a right triangle, the sum of the squares of the two sides that join at a right angle equals the square of the third side.
www.math.com /school/subject3/lessons/S3U3L4DP.html   (505 words)

 Figures and polygons
The sum of the angles of a triangle is 180 degrees.
One of the angles of the triangle measures 90 degrees.
A right triangle has the special property that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
www.mathleague.com /help/geometry/polygons.htm   (610 words)

 Relations and sizes - Right triangle facts - First Glance   (Site not responding. Last check: 2007-11-07)
The right triangle is one of the most important geometrical figures, used in many applications for thousands of years.
He treated each side of a right triangle as though it were a square and discovered that the total area of the two smaller squares is equal to the area of the largest square.
where c is the hypotenuse and a and b are the other two legs of the triangle.
www.math.com /school/subject3/lessons/S3U3L4GL.html   (112 words)

 Right Triangle Trigonometry
The hypotenuse is across from the right angle.
In right triangle ABC, leg BC=20 and angle B = 41ยบ.
The hypotenuse is always the largest side in a right triangle.
regentsprep.org /Regents/math/rtritrig/Ltrig.htm   (286 words)

 The Pythagorean Theorem
for a right triangle with sides of lengths a, b, and c, where c is the length of the hypotenuse.
Proposition: In right-angled triangles the square on the hypotenuse is equal to the sum of the squares on the legs.
Triangle 1 (green) is the right triangle that we began with prior to constructing CD.
jwilson.coe.uga.edu /emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html   (2131 words)

 Physics Help and Math Help - Physics Forums - Area of a right-angled triangle
In a given right-angled triangle, the length of the hypotenuse is 10 and the length of one of the heights is 6.
The triangle you describe is a 3-4-5 triangle, one of the most useful combinations of all right triangles.
Any triangle drawn in a circle with one edge forming the diameter of aforesaid circle is a right triangle, and further, the hypotenuse is the diameter, and the opposite angle is the right angle.
www.physicsforums.com /printthread.php?t=13375&pp=40   (1879 words)

 Triangle Details, Meaning Triangle Article and Explanation Guide
A central theorem is the Pythagorean theorem stating that in any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
A perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
www.e-paranoids.com /t/tr/triangle.html   (1810 words)

 Applications of Right Triangle Trigonometry
When one knows one of the acute angles of a right triangle and the length of one of the sides, one can solve for the length of the other two sides using trigonometric functions of the given angle.
It is a convention that if a vertex of a triangle is denoted by an upper case letter, then the side opposite that vertex is denoted by the corresponding lower case letter.
The famous Pythagorean Theorem of antiquity states that the sum of the areas of the two squares constructed on the sides of a right triangle equals the area of the square constructed on the hypotenuse.
jwbales.home.mindspring.com /precal/part4/part4.5.html   (693 words)

 Pythagorean Theorem and its many proofs   (Site not responding. Last check: 2007-11-07)
In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle.
Let ABC be a right triangle, with the right angle at C. Draw the altitude from C to the hypotenuse; let P denote the foot of this altitude.
He also pointed out that it is possible to think of one of the right triangles as sliding from its position in proof #46 to its position in proof #48 so that its short leg glides along the long leg of the other triangle.
www.cut-the-knot.com /pythagoras/index.html   (6005 words)

 Triangles - Technical Analysis
Triangle patterns usually form part way through a strongly trending move and represent a congestive phase in the marketplace.
The symmetrical triangle is a neutral pattern, whereas the ascending right triangle is bullish and the descending right triangle is bearish.
The descending triangle is a flipped over ascending triangle with a flat bottom line and a declining upper line.
www.chartfilter.com /reports/c32c.htm   (540 words)

 5.1 Triangles
In an acute triangle all angles are acute.
Many formulas for an isosceles triangle of sides a, a, c can be immediately derived from those for a right triangle of legs a, ½c (see Figure 2, left).
For a right triangle the hypothenuse is the longest side opposite the right angle; the legs are the two shorter sides, adjacent to the right angle.
www.geom.umn.edu /docs/reference/CRC-formulas/node22.html   (704 words)

 Trigonometry: A Crash Review
For an isosceles triangle, the two angles opposite the sides with equal length (i.e., the two angles whose bounding sides have one of the two sides of equal length, and the side with different length) are equal.
Given a right triangle, the trig function values for the two acute angles [angles smaller than a right angle] can be computed without knowing the angles.
The horizontal side (on the x-axis) is A, and the vertical side (parallel to the y-axis) is O. The radius (length 1) is H. The slope of the hypotenuse H is tan(X).
www.zaimoni.com /Trig.htm   (5588 words)

 Hamilton - Math To Build On: Right Triangles
The three sides of a right triangle are represented by the variables a, b, and c.
The longest side of a right triangle is always directly across from the 90 degree angle.
Since the numbers on both sides of the = mark are the same, the 3-4-5 triangle is a right triangle.
mathforum.org /%7Esarah/hamilton/ham.rttriangles.html   (306 words)

 Topics in trigonometry:  The isosceles right triangle
Note that since the triangle is isosceles, then the angles at the base are equal.
Solve the isosceles right triangle whose side is 6.5 cm.
Since this is an isosceles right triangle, the only problem is to find the unknown hypotenuse.
www.themathpage.com /aTrig/isosceles-right-triangle.htm   (313 words)

 The Machinist's Friend right triangle module solves only right triangles.
The sum of the three angles of a Right Triangle will total 180 degrees and one of the angles will always be 90 degrees or square.
The length of the side opposite the 90 degree angle must be larger than the length of either of the other two sides.
When the triangle is calculated another triangle will be drawn on the inside of the large working triangle.
www.machinistsfriend.com /right.htm   (224 words)

 The Triangle Figure
When she placed an acute scalene triangle next to me on her desk, I remembered times as a student that I was asked to sketch an acute scalene triangle to investigate some triangle property.
To make an acute triangle, we can use the fact that the plane is divided into acute and obtuse regions by the sets of points which yield a right triangle.
These two reflections may be used to generate a total of four congruent triangles within the same pencil, as long as the third vertex of the initial triangle is not on either of the lines of reflection.
www.math.clemson.edu /~rsimms/triangle   (1573 words)

 SparkNotes: Solving Right Triangles: Right Triangle Review
A right triangle is a triangle with one right angle.
The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
The triangle above is the general form of the right triangles we'll study in these sections on solving right triangles.
www.sparknotes.com /math/trigonometry/solvingrighttriangles/section1.html   (406 words)

 Oblique Triangles   (Site not responding. Last check: 2007-11-07)
It could be an acute triangle (all threee angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).
The trigonometry of oblique triangles is not as simple of that of right triangles, but there are two theorems of geometry that give useful laws of trigonometry.
It looks like the Pythagorean theorem except for the last term, and if C happens to be a right angle, that last term disappears (since the cosine of 90° is 0), so the law of cosines is actually a generalization of the Pythagorean theorem.
aleph0.clarku.edu /~djoyce/java/trig/oblique.html   (1604 words)

 The Amazing... 3-4-5 Right Triangle   (Site not responding. Last check: 2007-11-07)
The 3-4-5 Right Triangle has been used in the development of all civilizations throughout recorded and unrecorded history (nearly some 6,000 years, more or less).
The 3-4-5 right triangle plays a fundamental role in all types of Land and Construction Surveying, Map making, Land development, and in many types of Engineering.
The rope was of such a length that it could be formed into the 3-4-5 right triangle so as to form right angles to square off the land, and the 5 cubit rod used to lay out distances along the surveyed boundary lines by laying it end to end.
www.bright.net /%7Edon4   (280 words)

 The right sphirical triangle   (Site not responding. Last check: 2007-11-07)
A right spherical triangle is one which has an angle equal to 90 degrees.
If a triangle has three right angles, we have the solution at once, for each of the sides is a quadrant or 90 degrees.
If a triangle has two right angles, the sides opposite these angles are quadrants, and the third angle is measured by its opposite side.
www.angelfire.com /nt/navtrig/B2.html   (334 words)

 Pythagorean Theorem/ Science in Ancient Artwork
It would appear that the 3-4-5 right triangle, and its multiples and variations, may have served as a basis for the ancient reckoning system of Mesoamerica.
Pythagoras is cited as having understood the manner in which the three sides of a right triangle are related.
PROP.- In a progression of 3-4-5 right triangles, the cube of the shorter leg equals the sum of the cubes of the three sides of the right triangle inmediately preceding it on the progression.
www.earthmatrix.com /Pitagor3.htm   (638 words)

 Right Triangle Applications
Right triangle geometry has many applications in the real world.
We have a right trianngle, and d is the hypotenuse.
The Pythagorean Theorem states that the sum of the squres of the legs of a right triangle is equal to the square of the hypotenuse.
jwilson.coe.uga.edu /EMT668/EMAT6680.Folders/Brooks/6690stuff/Righttriangle/Applications.html   (540 words)

 SPACE.com -- Doorstep Astronomy: The Summer Triangle
This huge, nearly isosceles triangle is composed of three of the brightest stars in the sky, each the brightest star in its own constellation.
The Summer Triangle is one of the favorite parts of the sky for most sky watchers, perhaps because of its sheer simplicity in contrast to overabundance of bright stars found in the wintertime sky.
But in a twist, the triangle is designated not as a summer star pattern, but rather, is described under the chapter "Autumn and Winter Stars," since, as the authors point out, the "big triangle" passes overhead on September evenings.
www.space.com /spacewatch/050617_summer_triangle.html   (1192 words)

A triangle may be classified by how many of its sides are of equal length.
one of the angles is a right angle—an angle of 90 degrees.
A right triangle may be isosceles or scalene.
www.factmonster.com /ipka/A0876325.html   (164 words)

 VIAS Encyclopedia: Incircle and Angle Bisectors of a Triangle   (Site not responding. Last check: 2007-11-07)
The angle bisectors of a triangle are the lines which cut the inner angles of a triangle into equal halves.
The angle bisectors are concurrent and intersect at the center of the incircle (incenter S).
Each side of a triangle is cut by the corresponding angle bisector into two segments whose lengths are related to the lengths of the adjacent sides:
www.vias.org /encyclopedia/geom_triangle_angle_bisector.html   (125 words)

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