The known task about the parties of a rectangular triangle from school geometry is the cornerstone of many geometrical theorems and all course of trigonometry.
Instruction
1. Let the triangle with tops of A, B and C, and a corner of ABC — a straight line is set, that is it is equal to ninety degrees. The parties of AB and BC of such triangle are called legs, and the party of AC — a hypotenuse. For a start look at statements of the problem and define what sizes from the parties of a triangle are known to you and what party is required to be found. For the successful solution of a task it is necessary to know lengths of two of three parties of a triangle. Either lengths of two legs, or length of one of legs and hypotenuse length have to be known to you.
2. Length of the parties of a rectangular triangle pays off according to the theorem of the Ancient Greek mathematician Pythagoras. This theorem sets dependence between legs and a hypotenuse: the square of a hypotenuse is equal to the sum of squares of legs. In case it is required to find leg size (for example, AB leg), the formula for it will look so: AB = √ (AC² - BC²). It is possible to calculate it on the calculator, but in certain cases it is possible also in mind. For example, for a triangle with the parties of BC = 4 and AC = the 5th size of a leg of AB is also an integer and therefore it can be easily calculated on the given formula. AB = √ (25 - 16) = 3.
3. If it is required to find hypotenuse length, then it can be done on the following formula brought out of Pythagorean theorem: AC = √ (AB² + BC²). So, for a triangle with the parties of AB = 5 and BC = 12, we receive result of AC = √ (25 + 144) = 13. Depending on statements of the problem use the received result in further calculations or write as your answer.