How to find a triangle catat

Cathet is the side of the rectangular triangle, which adjacent to the corner of 90˚. The side opposite the direct angle is hypotenuse. Having data about other sides of the rectangular triangle or the values \u200b\u200bof the angles, you can determine the length of the unknown category.

Having the values \u200b\u200bof the length of the second category and hypotenuses, one can calculate the second catat on the Pythagora theorem. The length of the unknown category is equal to the square root of the sink of hypotenuse and the square of the second category: a \u003d √ (C²-B²).

It is possible to determine the catat if one of the angles of the rectangular triangle are known, which is not 90˚. Suppose there is an angle value α. Then the sinus α will be equal to the ratio of an opposite category to the magnitude of the hypotenuse (Sin α \u003d b / c), and the cosine α-ratio of the adjacent category to the hypothenus value (COS α \u003d A / C). So B \u003d C * SIN α, a \u003d C * COS α. The values \u200b\u200bof cosine and sinuses, tangents and catangents of the corners are contained in Special Bradys Tables.

If the known value of the second category (b) and acute angle opposite it (α), the value of the desired category (a) will be equal to the ratio of the length of the category B to the tangent of the angle α: a \u003d b / Tg α.

If the value of the angle adjacent to the cathelet of this length is known, the unknown catat is equal to the length of the known, divided by the Cotanence of the angle: a \u003d b / ctg β.

With the existing length of hypotenuse (C) and an angle, located opposite the desired category (α), unknown catat (a) will be equal to the product of the hypotenuse on the sinus of this angle: a \u003d c * sin α.
If the value of the second angle is known, which goes to the cathelet A, the equation will take the following form: a \u003d C * COS β.

Suppose you have a value (k) of the ratio of the known category (b) to the desired (A). Then catat A will be equal to: a \u003d C / √ (k² + 1).

All these solutions are based on the Pythagoreo theorem and the definitions of trigonometric functions. Knowledge of ordinary algebra laws will allow solving almost any task from the geometry field.