The equilateral triangle is a triangle which all parties are equal, as follows from its name. This feature significantly simplifies finding of other parameters of a triangle, including its height.
It is required to you
- Length of the party of an equilateral triangle
Instruction
1. All corners are also equal in an equilateral triangle. The corner of an equilateral triangle, from here, is equal 180/3 = 60 degrees. It is obvious that as all parties and all corners of such triangle are equal, all its heights will also be equal.
2. In an equilateral triangle of ABC it is possible to carry out, for example, AE height. As the equilateral triangle is a special case of an isosceles triangle, and AB = AC. Therefore, on property of an isosceles triangle height of AE will be at the same time a median (that is BE = EC) a triangle of ABC and BAC bisector (that is BAE = CAE).
3. Height of AE will be a leg of a rectangular triangle of BAE with AB hypotenuse. AB = an is length of the party of an equilateral triangle. Then AE = AB*sin(ABE) = a*sin(60o) = sqrt(3) *a/2. Therefore, for finding of height of an equilateral triangle, the nobility only length of its party is enough.
4. It is obvious that if the median or a bisector of an equilateral triangle is set, then it also will be its height.