The closed geometrical figure formed by two couples lying the friend opposite to the friend of parallel pieces of identical length, is called a parallelogram. And the parallelogram which all corners are equal 90 ° is called also a rectangle. In this figure it is possible to carry out two pieces of identical length connecting opposite tops there are diagonals. Length of these diagonals is calculated in several ways.
Instruction
1. If lengths of two adjacent parties of a rectangle (And yes C), diagonal length are known (C) it is very simple to define. You recognize that diagonal lies opposite to a right angle in the triangle formed by it and these two parties. It allows to apply Pythagorean theorem in calculations and to calculate diagonal length, having found a square root from the sum of the squared lengths of the known parties: With =v (And? + In?).
2. If length of only one party of a rectangle (A) and also size of a corner (?) which with it forms diagonal, then for calculation of length of this diagonal is known (C) it is necessary to use one of direct trigonometrical functions - a cosine. Divide length of the known party into a cosine of the known corner - it is and there will be required length of diagonal: With = And / cos (?).
3. If the rectangle is set by coordinates of the tops, then the problem of calculation of length of its diagonal will come down to finding of distance between two points in this system of coordinates. Apply Pythagorean theorem to a triangle which is formed by diagonal projections to each of coordinate axes. Let's say the rectangle in two-dimensional coordinates is formed by A tops (X?; Y?), B (X?; Y?), C (X?; Y?) and D (X?; Y?). Then you need to calculate distance between points of A and C. Length of a projection of this piece to axis X will be equal to the module of a difference of coordinates | to X? - X? |, and projections to axis Y - | Y? - Y? |. The corner between axes is equal 90 ° from what it follows that these two projections are legs, and length of the diagonal (hypotenuse) is equal to a square root from the sum of squares of their lengths: AC=v ((X? - X?)?+ (Y? - Y?)?).
4. For finding of diagonal of a rectangle in the three-dimensional system of coordinates act the same as in the previous step, having only added length of a projection to the third coordinate axis to a formula: AC=v ((X? - X?)?+ (Y? - Y?)?+ (Z? - Z?)?).