Ratios between the parties and corners of a rectangular triangle are considered in the section of mathematics which is called trigonometry. For finding of the parties of a rectangular triangle it is enough to know Pythagorean theorem, definitions of trigonometrical functions and to have any means for finding of values of trigonometrical functions, for example, the calculator or Bradis's tables. Let's consider below the main cases of problems of finding of the parties of a rectangular triangle.
It is required to you
- Calculator, Bradis's tables.
Instruction
1. Let's accept following designations: with – hypotenuse length (the parties, opposite to a right angle); a, b are lengths of legs (the parties adjacent to a right angle); A – corner, opposite to a leg; In – a corner, opposite to b leg.
2. In case are known to you a hypotenuse with and one of legs (for example, a leg a), the second leg it is possible to calculate from Pythagorean theorem: b=sqrt(с^2-а^2). Hereinafter "sqrt" is operation of extraction of a square root, "^2" - operation of squaring.
3. If both legs are known, the hypotenuse is also from Pythagorean theorem: with =sqrt(а^2+b^2).
4. If to you one of acute angles is set, for example, A, and a hypotenuse, then legs it is possible to find from definitions of the main trigonometrical functions: = c*sin (A), b = c*cos(A).
5. If one of acute angles, for example, of A, and one of legs, for example, an is set, then the hypotenuse and other leg are calculated from ratios: b=a*tg(A), c=a*sin(A).