Hypotenuse call the longest of the parties in a rectangular triangle therefore it is not surprising that this word is translated from Greek as "tense". This party always lies opposite to a corner in 90 °, and the parties forming this corner are called legs. Knowing lengths of these parties and size of acute angles in different combinations of these values it is possible to calculate also length of a hypotenuse.
Instruction
1. If lengths of both legs of a triangle are known (And yes C), use for finding of length of a hypotenuse (C) the mathematical postulate, most, perhaps, known on our planet, - Pythagorean theorem. It says that the square of length of a hypotenuse is equal to the sum of squares of lengths of legs from what it follows that you should calculate a square root from the sum of the squared lengths of two known parties: With = √ (And² + In²). For example, if length of one leg is equal to 15 centimeters, and another - to 10 centimeters, then length of a hypotenuse will be about 18.0277564 centimeters as √ (15²+10²)= √ (225+100) = √325≈18.0277564.
2. If length only of one of legs (A) in a rectangular triangle and also the size of the corner lying opposite to it (α), then hypotenuse length is known (C) it is possible to define by one of trigonometrical functions - a sine. For this purpose divide length of the known party into a sine of the known corner: With = And / sin(α). For example, if length of one of legs is equal to 15 centimeters, and corner size in top of a triangle opposite to it is 30 °, then length of a hypotenuse will be equal to 30 centimeters as 15/sin (30 °) =15/0.5=30.
3. If in a rectangular triangle the size of one of acute angles (α) and length of the leg (B) adjoining to it, then for calculation of length of a hypotenuse is known (C) it is possible to use other trigonometrical function - a cosine. You should divide length of the known leg into a cosine of the known corner: With = In / cos(α). For example, if length of this leg is equal to 15 centimeters, and the size of an acute angle, to it adjacent, is 30 °, then length of a hypotenuse will be about 17.3205081 centimeters as 15/cos (30 °) =15 / (0.5 * √ 3)=30 / √ 3≈17,3205081.