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How often are the longest angle in a triangle opposite to the longest side of a triangle?
Wiki User
∙ 12y ago
Pretty often, but not really common
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∙ 12y ago
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What is one of the 2 sides of the right triangle that form the right angle?
In a right angled triangle, there are three sides. The longest of these is referred to as the hypotenuse. This longest side is always the side opposite the right angle. The other two sides are most often referred to as the "opposite" and "adjacent" depending on which other angle you are looking at. If you look at an angle other than the right angle, it will touch two lines. One of these is the hypotenuse, the other is the adjacent. The line it is not touching is the opposite.
What does the maths term Pythagoras mean?
1) A famous mathematician. 2) The word is often used for the relationship a2 + b2 = c2. This applies to a right triangle, assuming "c" is the longest side (the side opposite the right angle).
What are five characteristics of a TRIANGLE?
Triangle (geometry) IINTRODUCTIONTriangle (geometry), geometric figure consisting of three points, called vertices, connected by three sides. In Euclidean plane geometry, the sides are straight line segments (see Fig. 1). In spherical geometry, the sides are arcs of great circles (see Fig. 2). See Geometry; Trigonometry. The term triangle is sometimes used to describe a geometric figure having three vertices and sides that are arbitrary curves (see Fig. 3).IIPLANE TRIANGLESA Euclidean plane triangle has three interior angles (the word interior is often omitted), each formed by two adjacent sides, as ÐCAB in Fig. 1, and six exterior angles, each formed by a side and the extension of an adjacent side, as ÐFEG in Fig. 4. A capital letter is customarily used to designate a vertex of a triangle, the angle at that vertex, or the measure of the angle in angular units; the corresponding lower case letter designates the side opposite the angle or its length in linear units. A side or its length is also designated by naming the endpoints; thus, in Fig. 1, the side opposite angle A is a or BC.An angle A is acute if 0° < A < 90°; the angle is right if A = 90°; and it is obtuse if 90° < A < 180°. Because the sum of the angles of a triangle is 180°, a triangle can have at most one angle that is equal to or greater than 90°. A triangle is acute if all three of its angles are acute, as in Fig. 1; it is right if it has one right angle, as in Fig. 5; and it is obtuse if it has one obtuse angle, as in Fig. 4.A triangle is scalene if no two of its sides are equal in length, as in Fig. 1; isosceles if two sides are equal, as in Fig. 6; and equilateral if all three sides are equal, as in Fig. 7. The side opposite the right angle in a right triangle, HK in Fig. 5, is called the hypotenuse; the other two sides are called legs. The two equal sides of an isosceles triangle are also called legs, and the included angle is called the vertex angle. The third side is called the base, and the adjacent angles are called the base angles.If two sides of a triangle are of unequal size, the angles opposite are of unequal size; the larger side is opposite the larger angle. In the same way, if two angles are unequal, the sides opposite are unequal. Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular). The side opposite a right angle or an obtuse angle is the longest side of the triangle. see Trigonometry: Law of Sines for the exact relation between the sizes of the angles and sides of a triangle.In any triangle, an altitude is a line through a vertex perpendicular to the opposite side or its extension, for example, DX in Fig. 8a and 8b. A median is the line determined by a vertex and the midpoint of the opposite side, AN in Fig. 9. An interior angle bisector is the line through a vertex bisecting the interior angle at the vertex, AR in Fig. 10; similarly, an exterior angle bisector bisects the exterior angle at the vertex, AV in Fig. 10. A perpendicular bisector is a line perpendicular to a side at its midpoint, HK in Fig. 11. The terms altitude, median, and interior angle bisectorare also often applied to the line segment determined by the vertex and the intersection with the opposite side or its extension.The three altitudes of a triangle meet in a common point called the orthocenter, O in Fig. 8a and 8b. The three medians meet in a point called the centroid, M in Fig. 9. The centroid divides a median through it into two segments, and the segment having a vertex as endpoint is always twice as long as the other segment. The three angle bisectors meet in a point called the incenter (I in Fig. 10), and the three exterior angle bisectors meet in three points called the excenters, U, V, Wof Fig. 10. The incenter and the three excenters are centers of circles tangent to the sides or side extensions of the triangle. The three perpendicular bisectors meet in a point called the circumcenter, H in Fig. 11, which is the center of a circle passing through the three vertices.If a, b, c are the three sides of a triangle, and ha is the altitude through vertex A, the semiperimeter s is given by the formula s = y (a + b + c), and the area K by the formula K = yaha. Many other formulas interrelate the various parts of a triangle.IIISPHERICAL TRIANGLESMany properties of plane triangles have analogues in spherical triangles, but the differences between the two types are important. For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle. A spherical triangle with one, two, or three right angles is called a rectangular, birectangular, or trirectangular triangle. A spherical triangle in which one, two, or three sides are quadrants (quarter circumferences) is called a quadrantal, biquadrantal, or triquadrantal triangle.If two sides of a triangle are of unequal size, the angles opposite are of unequal size; the larger side is opposite the larger angle. In the same way, if two angles are unequal, the sides opposite are unequal. Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular). The side opposite a right angle or an obtuse angle is the longest side of the triangle.
What is the definition for leg of a triangle?
There is no formal definition: it is any side of a triangle. Often, if the triangle has a horizontal base, then it is one of the sloped sides. In a right angled triangle, it is one of sides adjacent to the right angle. In an isosceles triangle, it is one of the equal sides.
Is there such thing as a triangle with no right angles?
Of course. A triangle with a right angle is a very special case that you don't run intovery often, unless you happen to be doing a unit on right triangles in school.
What is one of the 2 sides of the right triangle that form the right angle?
In a right angled triangle, there are three sides. The longest of these is referred to as the hypotenuse. This longest side is always the side opposite the right angle. The other two sides are most often referred to as the "opposite" and "adjacent" depending on which other angle you are looking at. If you look at an angle other than the right angle, it will touch two lines. One of these is the hypotenuse, the other is the adjacent. The line it is not touching is the opposite.
Why hypotenuse more than other two sides?
We don't think about this very often, but it turns out that in any triangle, the order of the angles by length is the same as the order of the sides opposite them by length. What I mean is: -- the shortest side is opposite the smallest angle -- the medium side is opposite the medium angle -- the longest side is opposite the largest angle In a right triangle, the right angle has to be the largest angle(**). So the side opposite it ... called the hypotenuse ... has to be the longest side. ============================================================ (**) Here's why the right angle has to be the largest angle: In any triangle, the inside angles all add up to 180 degrees. In a right triangle, one of the angles is 90 degrees. That leaves only another 90 degrees to split up between the other two angles, so both of them must be less than 90 degrees.
What does the maths term Pythagoras mean?
1) A famous mathematician. 2) The word is often used for the relationship a2 + b2 = c2. This applies to a right triangle, assuming "c" is the longest side (the side opposite the right angle).
What are five characteristics of a TRIANGLE?
Triangle (geometry) IINTRODUCTIONTriangle (geometry), geometric figure consisting of three points, called vertices, connected by three sides. In Euclidean plane geometry, the sides are straight line segments (see Fig. 1). In spherical geometry, the sides are arcs of great circles (see Fig. 2). See Geometry; Trigonometry. The term triangle is sometimes used to describe a geometric figure having three vertices and sides that are arbitrary curves (see Fig. 3).IIPLANE TRIANGLESA Euclidean plane triangle has three interior angles (the word interior is often omitted), each formed by two adjacent sides, as ÐCAB in Fig. 1, and six exterior angles, each formed by a side and the extension of an adjacent side, as ÐFEG in Fig. 4. A capital letter is customarily used to designate a vertex of a triangle, the angle at that vertex, or the measure of the angle in angular units; the corresponding lower case letter designates the side opposite the angle or its length in linear units. A side or its length is also designated by naming the endpoints; thus, in Fig. 1, the side opposite angle A is a or BC.An angle A is acute if 0° < A < 90°; the angle is right if A = 90°; and it is obtuse if 90° < A < 180°. Because the sum of the angles of a triangle is 180°, a triangle can have at most one angle that is equal to or greater than 90°. A triangle is acute if all three of its angles are acute, as in Fig. 1; it is right if it has one right angle, as in Fig. 5; and it is obtuse if it has one obtuse angle, as in Fig. 4.A triangle is scalene if no two of its sides are equal in length, as in Fig. 1; isosceles if two sides are equal, as in Fig. 6; and equilateral if all three sides are equal, as in Fig. 7. The side opposite the right angle in a right triangle, HK in Fig. 5, is called the hypotenuse; the other two sides are called legs. The two equal sides of an isosceles triangle are also called legs, and the included angle is called the vertex angle. The third side is called the base, and the adjacent angles are called the base angles.If two sides of a triangle are of unequal size, the angles opposite are of unequal size; the larger side is opposite the larger angle. In the same way, if two angles are unequal, the sides opposite are unequal. Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular). The side opposite a right angle or an obtuse angle is the longest side of the triangle. see Trigonometry: Law of Sines for the exact relation between the sizes of the angles and sides of a triangle.In any triangle, an altitude is a line through a vertex perpendicular to the opposite side or its extension, for example, DX in Fig. 8a and 8b. A median is the line determined by a vertex and the midpoint of the opposite side, AN in Fig. 9. An interior angle bisector is the line through a vertex bisecting the interior angle at the vertex, AR in Fig. 10; similarly, an exterior angle bisector bisects the exterior angle at the vertex, AV in Fig. 10. A perpendicular bisector is a line perpendicular to a side at its midpoint, HK in Fig. 11. The terms altitude, median, and interior angle bisectorare also often applied to the line segment determined by the vertex and the intersection with the opposite side or its extension.The three altitudes of a triangle meet in a common point called the orthocenter, O in Fig. 8a and 8b. The three medians meet in a point called the centroid, M in Fig. 9. The centroid divides a median through it into two segments, and the segment having a vertex as endpoint is always twice as long as the other segment. The three angle bisectors meet in a point called the incenter (I in Fig. 10), and the three exterior angle bisectors meet in three points called the excenters, U, V, Wof Fig. 10. The incenter and the three excenters are centers of circles tangent to the sides or side extensions of the triangle. The three perpendicular bisectors meet in a point called the circumcenter, H in Fig. 11, which is the center of a circle passing through the three vertices.If a, b, c are the three sides of a triangle, and ha is the altitude through vertex A, the semiperimeter s is given by the formula s = y (a + b + c), and the area K by the formula K = yaha. Many other formulas interrelate the various parts of a triangle.IIISPHERICAL TRIANGLESMany properties of plane triangles have analogues in spherical triangles, but the differences between the two types are important. For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle. A spherical triangle with one, two, or three right angles is called a rectangular, birectangular, or trirectangular triangle. A spherical triangle in which one, two, or three sides are quadrants (quarter circumferences) is called a quadrantal, biquadrantal, or triquadrantal triangle.If two sides of a triangle are of unequal size, the angles opposite are of unequal size; the larger side is opposite the larger angle. In the same way, if two angles are unequal, the sides opposite are unequal. Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular). The side opposite a right angle or an obtuse angle is the longest side of the triangle.
What is the definition for leg of a triangle?
There is no formal definition: it is any side of a triangle. Often, if the triangle has a horizontal base, then it is one of the sloped sides. In a right angled triangle, it is one of sides adjacent to the right angle. In an isosceles triangle, it is one of the equal sides.
Pythagoras is often described as what?
"The father of numbers."Pythagoras was an ancient Greek mathematician famous for his theorem for a right angle triangle.
Is there such thing as a triangle with no right angles?
Of course. A triangle with a right angle is a very special case that you don't run intovery often, unless you happen to be doing a unit on right triangles in school.
What does sas mean in geometery?
In geometry, SAS stands for "side-angle-side," which refers to a method of proving congruence between two triangles. It states that if two sides and the included angle of one triangle are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent.
What are four ways you can prove two right triangles are congruent?
1. The side angle side theorem, when used for right triangles is often called the leg leg theorem. it says if two legs of a right triangle are congruent to two legs of another right triangle, then the triangles are congruent. Now if you want to think of it as SAS, just remember both angles are right angles so you need only look at the legs.2. The next is the The Leg-Acute Angle Theorem which states if a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. This is the same as angle side angle for a general triangle. Just use the right angle as one of the angles, the leg and then the acute angle.3. The Hypotenuse-Acute Angle Theorem is the third way to prove 2 right triangles are congruent. This one is equivalent to AAS or angle angle side. This theorem says if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, the two triangles are congruent. This is the same as AAS again since you can use the right angle as the second angle in AAS.4. Last, but not least is Hypotenuse-Leg Postulate. Since it is NOT based on any other rules, this is a postulate and not a theorem. HL says if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
What is the angle sum for a 3 sided polygon?
The sum of the three INTERIOR angles is 180 degrees. And a 3-sided polygon is often referred to as a 'Triangle'.
What are some things shaped like right triangles?
A folded napkin is often folded into a right triangle. The corners of walls can be shaped like a right angle.
What is the formula of tan x?
In a right triangle, where the angle "x" is adjacent to the hypotenuse, the tangent of that angle would be the length of the opposite side divided by the length of the adjacent side (not the hypotenuse). For instance, consider a right triangle with the following side lengths: A = 3 B = 4 C = 5 B is the hypotenuse. The tangent of the angle between sides A and C would be B/A, or 4/3. The tangent of the angle between sides B and C would be B/A, or 3/4. This is often taught with the memorisation acronym "SOHCAHTOA": (S)ine = (O)pposite / (H)ypotenuse (C)osine = (A)djacent / (H)ypotenuse (T)angent = (O)pposite / (A)djacent
