Two short parties of a rectangular triangle are called legs, and long - a hypotenuse. Projections of the short parties to long divide a hypotenuse into two pieces of different length. If there is a need for calculation of size of one of these pieces, then ways of the solution of a task entirely depend on offered in the conditions of a set of basic data.
Instruction
1. If hypotenuse lengths are specified in initial statements of the problem (C) and that leg (A) which projection (Expert) is required to be calculated then use one of properties of a triangle. Use that the average geometrical lengths of a hypotenuse and required projection is equal to leg length: And = √ (S*As). As the concept "geometrical average" is equivalent to "a root from the work", for finding of a projection of a leg square length of a leg and divide the received value into hypotenuse length: Expert = (And / √ C)² = And²/С.
2. If length of a hypotenuse is unknown, and only lengths of both legs are given (And yes C), (Expert) it is possible to involve Pythagorean theorem in calculation of length of the necessary projection. Express according to it hypotenuse length through lengths of legs √ (And² + In²) and substitute the received expression in a formula from the previous step: The expert = And²/√ (And² + In²).
3. If length of a projection of one of legs (Vs) and hypotenuse length is known (C), then the way of finding of length of a projection of other leg (Expert) is obvious - just take away the first from the second known size: Expert = S-Vs.
4. If lengths of legs are unknown, but their ratio (x/y) and also length of a hypotenuse (C) is given, then use couple of formulas from the first and third steps. According to expression from the first step, the ratio of projections of legs (Expert and Vs) will be equal to a ratio of squares of their lengths: Expert / Vs = x²/y². On the other hand, according to a formula from the previous step, the Expert + = S.V the first equality express to Vs length of an unnecessary projection through necessary and substitute the received value in the second formula: Expert + As*kh²/y² = Expert * (1 + x²/y²) = Page. Bring a formula of finding of the necessary projection of a leg out of this equality: The expert = With / (1 + x²/y²).
5. If length of a projection to a hypotenuse of one leg (Vs) is known, and length of the hypotenuse is not specified in conditions, but height (H) which is carried out from a right angle of a triangle will be given, then it is enough for calculation of length of a projection of other leg (Expert) too. Square height and divide into length of the known projection: Expert = N²/Вс.