The triangle is the figure consisting of three points which are not lying on one straight line and three pieces connecting these points in pairs. Points are called tops (are designated by capital letters), and pieces the parties (are designated by small letters) a triangle. Distinguish the following types of triangles: an acute triangle (all three corners sharp), an obtusangular triangle (one of corners stupid), a rectangular triangle (one of straight line corners), isosceles (two of its parties are equal), equilateral (all its parties are equal). It is possible to find the party of a triangle in different ways, but it will always depend on type of a triangle and basic data.
Instruction
1. Ratio of the parties and corners in rectangular triangle: Let ABC be a rectangular triangle, a corner With – a straight line, corners of A and B – sharp. Then according to definition of a cosine: the cosine of the angle of A is equal to the relation of an adjacent leg of BC to AB hypotenuse. A sine of the angle And is called the relation of an opposite leg of BC to AB hypotenuse. A tangent of angle And is called the relation of an opposite leg of BC to an adjacent AS.Iz of these definitions receive the following ratios: The leg, opposite a corner And, is equal to the work of a hypotenuse on a sine And, or is equal to the work of the second leg on a tangent And; The Leg adjacent to a corner And, is equal to the work of a hypotenuse on a cosine And; In a rectangular triangle any of the parties can be calculated on Pythagorean theorem if two others are known. Pythagorean theorem: the square of length of a hypotenuse is equal in a rectangular triangle to the sum of squares of lengths of legs.
2. Ratio of the parties in any triangle: Theorem of cosines. The square of any party of a triangle is equal to the sum of squares of two other parties without the doubled work of these parties on a cosine of the angle between them. Theorem of sine. The parties of a triangle are proportional to sine of opposite corners.