If the only known angle is 90°, and in the conditions given the lengths of two sides of trianglea square (b and c), determine which of them is the hypotenuse - it must be the side of the big sizes. Then use the Pythagorean theorem and calculate the length of the unknown side (a) square root of difference of squares of the lengths of larger and smaller parties: a = √(c2-b2). However, you can not figure out which side is the hypotenuse, and extract the root of the module of the difference of the squares of their lengths.
Knowing the length of the hypotenuse (c) and the angle (α) lying next to your sideand (a) use in the calculation of the trigonometric definition of the sine function through the sharp corners of rectangular tregon. This definition says that the sine of the known angle conditions are equal to the ratio between the lengths of the opposite legand the hypotenuse, and therefore, to calculate the desired values multiply the sine to the length of the hypotenuse: a = sin(α)*C.
If in addition the length of the hypotenuse (C) is given the value of the angle (β), adjacent to the desired leg (a) use the definition of another function - cosine. It sounds exactly the same, and therefore, before the calculation, simply replace the function notation and angle in the formula from the previous step: a = cos(β)*C.
The cotangent function will help calculate the length of sidea (a), if the conditions the previous step replaced by a second hypotenuse legom (b). By definition, the value of this trigonometric function equal to the ratio of the lengths of the legs, so multiply the cotangent of an angle is known on the length of the known sides: a = ctg(β)*b.
Use the tangent to calculate the length of sidea (a), if the conditions is the value of angle (α) lying in the opposite apex of the triangleof the polygon, and the length of the second legand (b). According to the definition of the tangent is known of the conditions of an angle is the ratio of the length of the required side to the length of the known legand, therefore, multiply the value of this trigonometric function from a given angle to the length of the known sides: a = tg(α)*b.
Advice 2: How to find the cotangent of an angle
The cotangent is one of the trigonometric functions derivative of sine and cosine. It is an odd periodic (period equal to PI) and not continuous (breaks at points that are multiples of the number PI) function. To calculate its value can be the largest angle, according to the known lengths of the sides of the triangle, the values of sine and cosine and in other ways.
If you are aware of the value of the angle, calculate the value totangent , for example, using a standard calculator Windows. To run it open the main menu, type keyboard "ka" and press Enter. Then set the calculator in engineering mode - select the item with the same name under "View" menu or use the shortcut Alt + 2.
Enter value of angle in degrees. Separate buttons for the function cotangent is not provided, so first find the tangent (click tan), and then divide the resulting value unit (click the button 1/x).
If the value of the tangent of the desired angle is given in terms of the problem to compute the cotangent to know the magnitude of this angle is not necessary - simply divide the unit number representing the tangent: ctg(α) = 1/tg(α). But you can certainly first determine the degree measure of the angle using the inverse tangent function the inverse tangent, and then to compute the well-known cotangent of the angle. In General this solution can be written as: ctg(α) = arctg(tg(α)).
Under certain conditions the values of the sine and cosine of the desired angle is also no need to determine its value. To find the cotangent divide the second number by the first: ctg(α) = cos(α)/sin(α).
If the conditions of the problem to find the cotangent given only one value (sine or cosine), convert the formula in the previous step, on the basis of linking their ratio sin2(α) + cos2(α) = 1. It is possible to Express one function through another: sin(α) = √(1-cos2(α)) and cos(α) = √(1-sin2(α)). Substitute the appropriate equality into the formula: ctg(α) = cos(α)/√(1-cos2(α)) or ctg(α) = √(1-sin2(α))/sin(α).
Without information on the size of the angle or the corresponding values of trigonometric functions also allows you to calculate the cotangent in the presence of some additional data. For example, it can be done if the angle the cotangent of which you want to calculate, lies in one of the vertices of a right triangle with known lengths of the legs. In this case, calculate the fraction, the numerator of which put the length to that of the other two sides adjacent to the appropriate corner, and the length of the second place in the denominator.