Advice 1: How to find the length of the hypotenuse

The hypotenuse is the largest side of a right triangle. It is located opposite the angle to ninety degrees and is usually known since the seventh grade, the theorem of the ancient Greek scientist Pythagoras. It sounds like this: "the square of the hypotenuse isequal to the sum of the squares of the other two sides". Looks menacing, but is easily solved. There are other methods of finding the lengths of the sides of the triangle.
How to find the length of the hypotenuse
You will need
  • Table Bradis, calculator.
Instruction
1
If you want to calculate the hypotenuse by the Pythagorean theorem, use the following algorithm:- Determine the triangle which sides are legs and which is the hypotenuse. The two sides forming the angle to ninety degrees and have each of the the remaining third side of the triangle is the hypotenuse. (see figure)- Lift the second degree, each leg of this triangle, that is, multiply their value by yourself. Example 1. Let we need to calculate the hypotenuse if one leg of the triangle is 12 cm and another 5 cm first, the squares of the legs is equal to: 12*12=144 cm and 5*5 = 25 cm Next, determine the sum of squares of other two sides. A certain number is the square of the hypotenuse, then you need to get rid of the degree numbers to find the length of this side of the triangle. To do this, remove from under the square root value of the sum of squares of other two sides. Example 1. 144+25=169. The square root of 169 is 13. Therefore, the length of the hypotenuse is equal to 13 cm.
2
Another method of calculating the length of the hypotenuse is in terms of sine and cosine of angles in the triangle. By definition, the sine of the angle alpha is the ratio of the opposite leg to the hypotenuse. That is, looking at the figure, sin a = SV / AV. Hence, the hypotenuse AB = DM / sin a.Example 2. If the angle a is 30 degrees, and opposite him the side - 4 cm Need to find the hypotenuse. Solution: AB = 4 cm/ sin 30 = 4 cm / 0.5 = 8 cm Answer: the length of the hypotenuse is equal to 8 cm.
3
The same method of finding the hypotenuse from the definition of the cosine of the angle. The cosine of an angle is the ratio adjacent thereto of the leg and the hypotenuse. That is, cos a = AC/AB, hence AB = AC/cos. Example 3. In triangle ABC, AB is the hypotenuse, angle ABC is 60 degrees, side AC is 2 cm Find AB.
Solution: AB = AC/cos 60 = 2/0,5 = 4 cm answer: the hypotenuse is 4 cm in length.
Useful advice
When finding the values of the sine or cosine of an angle use a table of sines and cosines, or table Bradis.

Advice 2: How to find the length of the hypotenuse in a right triangle

Call the hypotenuse the longest side in a right triangle, therefore, not surprising that in the Greek language this word is translated as "stretched". This side is always opposite the angle to 90° and the sides that form the angle are called the legs. Knowing the lengths of these sides and the magnitude of the acute angles in different combinations of these values, we can calculate the length of the hypotenuse.
How to find the length of the hypotenuse in a right triangle
Instruction
1
If you know the lengths of both legs of the triangle (A and b), then use to find the length of the hypotenuse (C) is probably the most famous on the planet a mathematical postulate - the Pythagorean theorem. It States that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, from which it follows that you should calculate the square root of the sum of squared lengths of two known sides: C=√(A2+B2). For example, if the length of one leg is 15 inches and the other 10 centimeters, the length of the hypotenuse will be approximately 18,0277564 centimeters, as √(152+102)=√(225+100)= √325≈18,0277564.
2
If you know the length of only one of the legs (A) in a right triangle, and the angle lying opposite it (α), the length of the hypotenuse (C) can be determined using one of the trigonometric functions - sine. To do this, divide the length of the known side by the sine of the known angle: C=A/sin(α). For example, if the length of one of the legs is equal to 15 centimeters and the angle at the opposite vertex of the triangle is 30°, the length of the hypotenuse is equal to 30 centimeters, as 15/sin(30°)=15/0,5=30.
3
If in a right triangle, we know the value of one of the acute angles (α) and the length of the adjacent leg (B), to calculate the length of the hypotenuse (C) you can use another trigonometric function, the cosine. You should divide the length of the known leg to the cosine of the known angle: S=V/ cos(α). For example, if the length of this side is 15 centimeters and the magnitude of the acute angle, the Annex, is 30°, the length of the hypotenuse will be approximately 17,3205081 centimeters, as 15/cos(30°)=15/(0,5*√3)=30/√3≈17,3205081.
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