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In the Pythagorean theorem, the formula is expressed as ( a^2 + b^2 = c^2 ). Here, ( a ) and ( b ) represent the lengths of the two legs of a right triangle, while ( c ) represents the length of the hypotenuse, the side opposite the right angle. This theorem establishes the relationship between the sides of a right triangle, indicating that the sum of the squares of the legs equals the square of the hypotenuse.

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What is a fractions used to represent?

Pieces of something that are smaller than the whole thing.


What is a checker piece called?

What are the checker pieces called and what do they represent?


How do you figure out the length of one side of a triangle with the length of other two sides?

C^2=A^2+B^2. Pythagorean theorem. Note that this is only true for Right triangles (one of the angles is 90°). Side C is the longest side and is opposite the 90° angle. For any other triangle, you need at least 3 pieces of information (2 sides and an angle, or 2 angles and a side) to find the other parts of the triangle. In a right triangle, if you know 2 sides, then you have 3 pieces of info (one of the angles is 90°). For non-right triangles, you can use the Law of Sines or Law of Cosines to solve for the unknown information.


Using 2 pieces of string stretched to the same tension Pythagoras?

When two pieces of string are stretched to the same tension, they can form a right triangle if they are arranged at angles to each other. Using Pythagoras' theorem, the resultant tension in a direction can be calculated by treating the two tensions as perpendicular vectors. The formula ( R = \sqrt{T_1^2 + T_2^2} ) can be applied, where ( T_1 ) and ( T_2 ) are the tensions in the strings. This allows for the determination of the overall tension and direction of the combined forces acting on the system.


How many pieces of pie can you make with 10 cuts?

With 10 straight cuts, you can create a maximum of 56 pieces of pie. This is based on the formula for the maximum number of pieces ( P(n) = \frac{n(n + 1)}{2} + 1 ), where ( n ) is the number of cuts. For 10 cuts, substituting into the formula gives ( P(10) = \frac{10 \times 11}{2} + 1 = 56 ).

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