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A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, the area is [ 1] It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his ...
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...
The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base , and the hypotenuse is the side of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem ( a 2 ) 2 + h 2 = a 2 {\displaystyle \left({\frac {a}{2}}\right)^{2}+h^{2}=a^{2}} so that h = 3 2 ...
The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between base and apex is the height. The area of a triangle equals one half the product of height and base length.
Altitude (triangle) The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex. This line containing the opposite side is called the extended base ...
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular forming a right angle ( 1⁄4 turn or 90 degrees ). The side opposite to the right angle is called the hypotenuse (side in the figure). The sides adjacent to the right angle are called ...
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]
Triangulation. Estimating the height of a mountain using triangulation. A triangulation station signed by iron rod [ 1] In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points.