Legs call two short parties of a rectangular triangle making that its top which size is equal 90 °. The third party in such triangle is called a hypotenuse. All these parties and corners of a triangle are connected among themselves by certain ratios which allow to calculate leg length if several other parameters are known.
Instruction
1. Use Pythagorean theorem for calculation of length of a leg (A) if length of two other parties (B and C) a rectangular triangle is known. This theorem claims that the sum of the squared lengths of legs is equal to a hypotenuse square. From this follows that length of each of legs is equal to a square root from the difference of squares of lengths of a hypotenuse and the second leg: A= √ (C²-B²).
2. Use definition of the direct trigonometrical sine function for an acute angle if the corner size (α) lying opposite the calculated leg and length of a hypotenuse (C) is known. This definition claims that the sine of this known corner is equal to the relation of length of a required leg to hypotenuse length. It means that length of a required leg is equal to the work of length of a hypotenuse on a sine of the known corner: A=C∗sin(α). For the same known sizes it is possible to use also definition of function a cosecant and to calculate the necessary length, having divided hypotenuse length into a cosecant of the known corner of A=C/cosec(α).
3. Involve definition of direct trigonometrical function a cosine if except length of a hypotenuse (C) also the size of an acute angle (β), adjacent to a required leg is known. The cosine of this corner is defined as a ratio of lengths of a required leg and a hypotenuse, and from this it is possible to draw a conclusion that length of a leg is equal to the work of length of a hypotenuse on a cosine of the known corner: A=C∗cos(β). It is possible to use function definition a secant and to calculate the necessary value, having divided hypotenuse length into a secant of the known corner of A=C/sec(β).
4. Bring the necessary formula out of similar definition for derivative trigonometrical function a tangent if except the size of the acute angle (α) lying opposite a required leg (A) length of the second leg (B) is known. A tangent opposite to a required leg of a corner call the relation of length of this leg to length of the second leg. Means, required size will be equal to the work of length of the known leg on a tangent of the known corner: A=B∗tg(α). It is possible to bring out of the same known sizes also other formula if to use function definition a cotangent. In this case for calculation of length of a leg it will be necessary to find a ratio of length of the known leg to a cotangent of the known corner: A=B/ctg(α).