Such triangle which has one of straight line corners is considered rectangular. The party of a triangle located opposite to a right angle is called a hypotenuse, and two other parties - legs. To find lengths of the parties of a rectangular triangle, it is possible to use in several ways.
Instruction
1. It is possible to learn the size of the third party, knowing lengths of two other parties of a triangle. It can be executed by means of Pythagorean theorem which says that the square of a hypotenuse of a rectangular triangle is equal to the sum of squares of its legs. (a² = b² + with²). From here it is possible to express lengths of all parties of a rectangular triangle: b² = a² - with²; with² = a² - b²К to an example, at a rectangular triangle is known a hypotenuse length (18 cm) and one of legs, for example c (14 cm). To find length of other leg, it is required to make 2 algebraic actions: with² = 18² - 14² = 324 - 196 = 128 SMS = √128 smotvt: length of the second leg is √128 cm or, about, 11.3 cm
2. It is possible to resort to other way if length of a hypotenuse and size of one of acute angles of this rectangular triangle are known. Let length of a hypotenuse be equal to c, one of acute angles is equal α. In that case, it will be possible to find 2 other parties of a rectangular triangle by means of the following formulas: a = с*sinα; b = с*cosα.Можно to give an example: length of a hypotenuse is equal to 15 cm, one of acute angles is equal to 30 degrees. For finding of lengths of two other parties it is necessary to perform 2 operations: a = 15*sin30 = 15*0.5 = 7.5 smb = 15*cos30 = (15 * √ 3)/2 = 13 cm (approximately)
3. The most uncommon way to find length of the party of a rectangular triangle is to express it from perimeter of this figure: P = a + b + c, where P - perimeter of a rectangular triangle. From this expression it is easy to express length of any of the parties of a rectangular triangle.