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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 ...
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 ...
v. t. e. Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [ 1 ] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths.
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 ...
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] [2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial ...
Interior angle Δθ = θ 1 −θ 2. The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines, which states that where is the angle between sides and . [ 45] When is radians or 90°, then , and the formula reduces to the usual Pythagorean theorem.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
The area of a triangle is half of one side times the height from that side: =. An equilateral triangle with a side of 2 has a height of √ 3 , as the sine of 60° is √ 3 /2 . The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base a {\displaystyle a} , and the hypotenuse is the side a ...