The geometrical figure consisting of three points which are not belonging to one straight line called tops and three pieces which are in pairs connecting them called by the parties is called a triangle. There is a set of tasks on finding of the parties and corners of a triangle by limited quantity of basic data, one of such tasks – finding of the party of a triangle on one of its parties and two corners.
Instruction
1. Let the triangle be constructed? ABCs are also known – the party of BC and corners?? and??. It is known that the sum of corners of any triangle is equal to 180?, therefore in a triangle? ABC corner?? it will be equal?? = 180? - (?? +??). It is possible to find the parties of AC and AB using the theorem of sine which glasitAB/sin?? = BC/sin?? = AC/sin?? = 2 * R where R is radius circumscribed about a triangle? ABC of a circle, then poluchayemr = BC/sin??, AB = 2 * R * sin??, AC = 2 * R * sin??. The theorem of sine can be applied at any these two corners and the party.
2. The parties it is set a triangle it is possible to find, having calculated its area on formules = 2 * R? * sin?? * sin?? * sin??, where R is calculated on formuler = by BC/sin??, R is radius circumscribed about a triangle? ABC of an otsyudatogd the party of AB can be found, having calculated height lowered on neyoh = by BC * sin??, from here on formula S = 1/2 * h * AB imeemAV = 2 * S/hanalogichnym can calculate in the way the party of AC.
3. If as corners external corners of a triangle are given?? and??, it is possible to find internal corners by means of the corresponding ratios?? = 180?-???? = 180?-???? = 180? - (?? +??). Further we act similar to the first two points.