The external corner of a triangle is adjacent to an internal corner of a figure. In the sum these corners at each of tops of a triangle make 180 ° and represent the developed corner.
Instruction
1. From the name it is obvious that the external corner lies outside a triangle. To imagine an external corner, prolong the party of a figure for top. The corner between continuation of the party and the second party of a triangle leaving this top will also be external for a triangle corner at this top.
2. It is obvious that to an acute angle of a triangle there corresponds the obtuse external angle. For an obtuse angle an external corner — a sharp, and external corner of a right angle — a straight line. Two corners with the general party and the parties belonging to one straight line are adjacent and in the sum make 180 °. If the triangle corner α is known for a condition, then the external corner, adjacent to it, β is defined so: β=180 °-α.
3. If the corner α is not set, but other two corners of a triangle are known, then their sum is equal to the size of a corner external in relation to a corner α. This statement follows from the fact that the sum of all corners of a triangle is equal 180 °. In a triangle the external corner is more than internal corner not adjacent to it.
4. If the-degree measure of a corner of a triangle is not set, but from a ratio of the parties trigonometrical dependences are known, then according to these data it is also possible to find an external corner: Sinα = Sin (180 °-α) Cosα = - Cos (180 °-α) tgα =-tg (180 °-α).
5. The external corner of a triangle can be defined if any internal corner is not set, and only the parties of a figure are known. From communications between elements of a triangle define one of trigonometrical functions of an internal corner. Calculate the corresponding function of a required external corner and according to trigonometrical tables of Bradis find his size in degrees. For example, from a formula of Square S=(b*c*Sinα)/2 define Sinα, and then an internal and external corner in a-degree measure. Or define Cosα from the theorem of cosines of a²=b²+c²-2bc*Cosα.