Hypotenuse is called the longest party of a rectangular triangle. It protivolezhit to the biggest corner, that is direct. Similar calculations are put into practice. Need to calculate a hypotenuse arises in construction - when calculating ladders, in geodesy and cartography — when determining extent of a slope. The similar task regularly arises also in everyday life. For example, to determine length of extensions for a tent.
It is required to you
- - a rectangular triangle with the set parameters;
- - calculator;
- - pencil;
- - ruler;
- - square;
- - Pythagorean theorem;
- - definitions of a sine and cosine.
Instruction
1. Construct a rectangular triangle. In statements of the problem either sizes of both legs, or length of a leg and the size of one of corners have to be given. Knowing these data and using their ratios, it is possible to calculate also all other parameters. Begin with creation of a triangle. It not only will help you with calculations, but also will give the chance to remember ways of the solution of similar tasks for very long time.
2. On the sheet of paper draw a horizontal straight line and postpone on it the size of one of legs. To the initial point of a piece carry out a perpendicular. Carry out the following constructions depending on what data you have. If you know to the size of both legs, on a perpendicular postpone the piece equal to length of the second. Connect the received point to the end of the first piece. Designate a right angle as With, and sharp — as And yes V. Oboznachte opposite to corners of the party as and, b and page.
3. If the leg and one of corners is known to you, draw just the same piece. To the initial point carry out a perpendicular, and from final postpone the set or calculated size of an adjacent corner. Designate a triangle and its elements just as in the previous case.
4. Knowing both legs, calculate a hypotenuse on Pythagorean theorem. It is equal to a square root from the sum of squares of legs, that is with = √ to a2+b2. This expression is a special case of the general formula of calculation of the party of a triangle. It is equal to a square root from the sum of squares two others the party, minus the doubled work of these parties on a cosine of the angle between them. That is with = √ a2+b2-2ab*cosC. As the cosine of a right angle is equal to zero, and his work on any number is equal to zero.
5. Knowing a leg and an opposite or adjacent corner, find a hypotenuse through a sine or a cosine. In the first case the formula will look as with = and / sinA where with — a hypotenuse, and — length of the known leg, And — an opposite corner. In the second case the expression can be presented as with = and / cosB where B is an adjacent corner.