Information on a median and one of the parties of a triangle is enough for finding of its other party if it is equilateral or isosceles. In other cases for this purpose it is necessary to know a corner between a median and height.
Instruction
1. The simplest case arises when in a statement of the problem the isosceles triangle with some party of an is given. Two sides of such triangle are equal, and all medians are crossed in one point. Besides, the median in isosceles triangle which is carried out to the basis is both height, and a bisector. Respectively, in a triangle of ABC there will be BHC triangle, and on Pythagorean theorem it will be possible to calculate HC - a half of the party of AC: HC= √ [(CB) ^2-(BH) ^2] Therefore, AC=2 √ [(CB) ^2-(BH) ^2] In an isosceles triangle a corner α=γ as it is shown in the drawing.
2. If the value of length of the median of an isosceles triangle which is carried out to its side is given in a statement of the problem solve a problem in a bit different way. First, the median is not perpendicular to figure side, and secondly, the dependence formula between a median and three parties looks as follows: √ 2 (c^2+b^2)-a^2По to this formula find ma= that party which the median halves.
3. If the triangle is wrong, then information on a median and the party insufficiently. It is necessary to know also a corner between a median and the party. To solve a problem, in the beginning find a half of the party of a triangle according to the theorem of cosines: c^2=a^2+b^2-2ab*cosγ, where with - the party which needs to be found. If it turns out so that using the theorem of cosines, it is possible to find only a half of the party then the calculated value is multiplied by two. For example, the median and the party, adjacent to it, between which there is a corner is given. The party opposite to a corner is halved by a median. Having calculated a half of the party according to the theorem of cosines, we will receive: BC = 2c, where with - 1/2 parties of BC
4. The solution of rectangular triangles is the same, as well as at any wrong triangle if its corners are not known to us, and the corner between a median and the party is given only. Having learned the second party, it is already possible to find also a third in Pythagorean theorem. Such tasks help to look for besides the parties and other parameters of triangles. The area and perimeter which are calculated on the set parties and corners concern them, for example.