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If is the radius of the incircle of the triangle, then the triangle can be broken into three triangles of equal altitude and bases , , and . Their combined area is A = 1 2 a r + 1 2 b r + 1 2 c r = r s , {\displaystyle A={\tfrac {1}{2}}ar+{\tfrac {1}{2}}br+{\tfrac {1}{2}}cr=rs,} where s = 1 2 ( a + b + c ...
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Fig. 1 Isosceles skinny triangle. In trigonometry, a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians.
Its surface area is four times the area of an equilateral triangle: = =. [7] The volume is one-third of the base times the height, the general formula for a pyramid; [7] this can also be found by dissecting a cube into a tetrahedron and four triangular pyramids. [8]
Scalene may refer to: A scalene triangle, one in which all sides and angles are not the same. A scalene ellipsoid, one in which the lengths of all three semi ...
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
A Heronian triangle, also known as a Heron triangle or a Hero triangle, is a triangle with integer sides and integer area. All Heronian triangles can be placed on a lattice with each vertex at a lattice point. [7] Furthermore, if an integer triangle can be place on a lattice with each vertex at a lattice point it must be Heronian.