"And we are told that the leg is shorter than the hypotenuse ..." These lines from a famous song that was played in the film "The Adventures of Electronics" is really true of Euclid's geometry. After the legs - are two sides forming an angle, degree measure is equal to 90 degrees. A hypotenuse - the longest "stretched" side that connects the two mutually perpendicular leg, and lies opposite the right angle. That is why to find the hypotenuse of Catete can only be in a right triangle, and if the leg is longer than the hypotenuse, then such a triangle would not exist.
How to find the hypotenuse of the Pythagorean theorem, if known, both leg
The theorem states that the square of the hypotenuse - it is nothing else than the sum of the squares of the legs: x ^ 2 + y ^ 2 \u003d z ^ 2, where:
- x - the first leg;
- y - a second leg;
- z - hypotenuse.
But we need to find a hypotenuse, not the square. To do this, remove the root.
The algorithm for finding the hypotenuse of two known cathetus:
- Designate for yourself where the legs, but where the hypotenuse.
- Lift the first leg of the square.
- Lift the second leg of the square.
- Fold the obtained values.
- Take the square root of the number obtained in step 4.
How to find the hypotenuse via sine, if known, and the acute angle leg lying against it
Known relationship to acute angle leg lying against it, equal to the hypotenuse: a / sin A \u003d c. This is a consequence of the definition of sine:
Opposing relationship to the hypotenuse leg: sin A \u003d a / c, where:
- a - the first leg;
- A - an acute angle opposite cathetus;
- c- hypotenuse.
The algorithm for finding the hypotenuse of sines:
- Label for themselves known leg and an opposite corner.
- Divide the cathetus opposite to the angle.
- Get the hypotenuse.
How to find the hypotenuse through cosine, if known cathetus and the acute angle adjacent to it
The ratio of the known category to the acute adjacent corner is equal to the hypotenuse of A / COS B \u003d C. This is a consequence of cosine definition: the ratio of the adjacent catech for hypotenuse: COS B \u003d A / C, where:
- a - second catat;
- B is a sharp angle, adjacent to the second cathelet;
- c-hypotenuse.
Algorithm for the location of hypotenuses on the cosine theorem:
- Indicate for yourself the famous catat and the corner prigible.
- Divide the catt on the prigular angle.
- Get the hypotenuse.
How to find a hypotenuse with the help of an "Egyptian triangle"
"Egyptian triangle" is a three numbers, knowing which you can save time to find a hypotenuse or even other unknown category. The triangle has such a name, since in Egypt some numbers symbolized the gods and were the basis for the structure of the pyramids and other different structures.
- The first three numbers: 3-4-5. Katenets are equal to 3 and 4. Then hypotenuse will necessarily be equal to 5. Check: (9 + 16 \u003d 25).
- The second triple numbers: 5-12-13. Here, kartettes are also equal to 5 and 12. Therefore, hypotenuse will be equal to 13. Check: (25 + 144 \u003d 169).
Such numbers help even when they are separated or multiplied by some single number. If the katenets are 3 and 4, then the hypotenuse will be equal to 5. If multiplying these numbers by 2, then the hypotenuse is multiplied by 2. For example, the three numbers of 6-8-10 will also be approached under the Pythagore theorem and can not be given by the hypotenuse if you Remember such top three numbers.
Thus, to find hypotenuses by known categories can be 4 ways. The most optimal option is the Pythagora theorem, but also did not hurt to remember the top three numbers that make up the "Egyptian triangle", because you can save a lot of time if you get so values.
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