The square triangle is called a rectangular triangle more precisely. Ratios between the parties and corners of this geometrical figure in detail are considered in mathematical discipline of trigonometry.
It is required to you
- - sheet of paper;
- - handle;
- - Bradis's tables;
- - calculator.
Instruction
1. Find partyrectangulartriangle by means of Pythagorean theorem. According to this theorem, the square of a hypotenuse is equal to the sum of squares of legs: s2 = a2+b2, where with – a hypotenuse of a triangle, an and b – its legs. To apply this equation, it is necessary to know length of any two parties of a rectangular triangle.
2. If the sizes of legs are under the terms set, find hypotenuse length. For this purpose by means of the calculator take a square root from the sum of legs, previously square each of which.
3. Calculate length of one of legs if the sizes of a hypotenuse and other leg are known. By means of the calculator take a square root from the difference of a hypotenuse in a square and the known leg which is also squared.
4. If in a task the hypotenuse and one of acute angles, adjacent to it, are set, use Bradis's tables. Values of trigonometrical functions for a large number of corners are given in them. Use the calculator with functions of a sine and cosine and also theorems of trigonometry which describe ratios between the parties and corners of a rectangular triangle.
5. Find legs by means of the main trigonometrical functions: a = c*sin α, b = c*cos α, where and – the leg opposite to a corner α, b – the leg adjacent to a corner α. In this way count the size of the parties of a triangle if the hypotenuse and other acute angle are set: b = c*sin β, a = c*cos β where b is the leg opposite to a corner β, and – the leg adjacent to a corner β.
6. In case the leg of an and an acute angle, adjacent to it, β is known, do not forget that the sum of acute angles is always equal in a rectangular triangle 90 °: α + β = 90 °. Find value of a corner opposite to a leg and: α = 90 ° – β. Or use trigonometrical formulas of reduction: sin α = sin (90 ° – β) = cos β; tg α = tg (90 ° – β) = ctg β = 1/tg β.
7. If the leg and and an acute angle, opposite to it, α, by means of Bradis's tables is known, the calculator and trigonometrical functions calculate a hypotenuse on a formula: c=a*sin α, leg: b=a*tg α.