School geometrical tasks quite often nonplus adults, especially if it is necessary to solve them in real life. For example, during the performing of repair work, design of furniture, work with computer programs. In all listed cases it can be necessary to find a corner between the set sides.
Instruction
1. First of all, remember that you know about a straight line. A straight line – one of the most important basic concepts in geometry. This distance between two points. It is set on the plane by Ax equation + By = C. In this equation of A/V it is equal to a straight line inclination tangent of angle, that is slope of a straight line. Often it is required to find a corner between figure sides in tasks.
2. We want to note initially that in order that it is correct to calculate a corner between sides of two straight lines, simple knowledge of geometry will be necessary. For this purpose it is possible just to take the school textbook on geometry and to repeat the forgotten material, in particular on the set subject a little.
3. Two direct Ax+By=C and Dx+Ey=F are Let's say given. To find a corner between sides of these straight lines, it is necessary to make a number of the following actions.
4. Express tilt angle coefficient from these equations of straight lines. For the first direct such coefficient will be equal to A/B, and for the second - according to D/E. That was more evident, we will show on examples. So if the straight line equation 4x+6y=20, respectively, the coefficient of a corner is equal to 0.67. If the equation of the second straight line - 3x+5y=3, the coefficient of a tilt angle is equal to-0.6.
5. Find a tilt angle of each of straight lines. For this purpose it is necessary to count an arctangent from the received slope. So if to take on the given example, arctg 0.67 will be equal 34 degrees, and arctg-0.6 is minus 31 degrees. Thus, one of straight lines has positive slope, and the second - negative. The corner between these straight lines will equal to the sum of absolute values of these corners. If both coefficients negative or both positive, a corner between sides are by taking away from bigger smaller.
6. Find a corner between sides. The corner between sides will be equal in our example 65 degrees (|34| + |-31| = 34 + 31).
7. It is necessary to know that the period of trigonometrical function a tangent (tg) is equal to 180 degrees and consequently, the tilt angle of such straight lines on the module cannot exceed this value.
8. When slopes are among themselves equal in a case, the corner between sides of such straight lines will be equal to zero as straight lines either will be parallel each other, or will coincide.