Hypotenuse – the mathematical term which is found by consideration of rectangular triangles. It is the greatest of its parties, opposite to a right angle. It is possible to calculate hypotenuse length in different ways, including on Pythagorean theorem.
Instruction
1. The triangle is the simplest closed geometrical figure consisting of three tops, corners and the parties, each of which has the name. A hypotenuse and two legs – the parties of a rectangular triangle which lengths are connected among themselves and with other sizes various formulas.
2. Most often to calculate hypotenuse length, the task is reduced to application of Pythagorean theorem which sounds so: the square of a hypotenuse is equal to the sum of squares of legs. Therefore, its length is calculation of a square root from this sum.
3. If only one leg and size of one of two corners which are not straight lines is known, then it is possible to use trigonometrical formulas. Let's assume, the triangle of ABC in which AC=c is a hypotenuse, AB=a and BC=b – legs, α – a corner between an and c, β – a corner between b and c is given. Then: c = a/cosα = a/sinβ = b/cosβ = b/sinα.
4. Solve a problem: to find hypotenuse length if it is known that AB=3 and the corner of BAC at this party is equal 30 °. ReshenieIspolzuyte trigonometrical formula: AC = AB/cos30 ° = 3•2/√ 3 = 2•√3.
5. It was the simple example on finding of the greatest party of a rectangular triangle. Solve following: to determine hypotenuse length if BH height which is carried out to it from opposite top is equal to 4. It is known also that height divides the party into pieces of AH and HC, and AH=3.
6. ReshenieOboznachte unknown part of a hypotenuse of HC=x. As soon as you find x, will be able to calculate also length of a hypotenuse. So, AC=x+3.
7. Consider AHB triangle - it rectangular by determination of height. You know lengths of two of its legs, so can find a hypotenuse of a which is a leg of a triangle of ABC: a= √ (AH² + BH²) = √ (16+9) = 5.
8. Pass to other rectangular triangle of BHC and find its hypotenuse which is equal to b, i.e. the second leg of a triangle of ABC: b² = 16 + x².
9. Return to a triangle of ABC and write down Pythagoras's formula, work out the equation relatively x: (x+3)² = 25 + (16 + x²) x² + 6•x + 9 = 41 + x² → 6•x = 32 → x=16/3.
10. Substitute x and find a hypotenuse: AC = 16/3 + 3 = 25/3.