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In mathematics the Pythagorean theorem, also known as pythagoras theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.” Stephanie J. Morris says “This famous theorem is named for the greek mathematician and philosopher, Pythagoras. Pythagoras founded the pythagorean school of mathematics in cortona, a greek seaport in southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his student”.

The pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. If the lengths of the legs are A and B, and the length of the hypotenuse is C, then, a^2 +b^2=c2. There are many different proofs of this theorem.

They fall in four categories.

Those based on linear relations: the algebraic proofs,

Those based upon comparison of areas: the geometric proofs,

Those based upon the vector operation,

Those based on mass and velocity:the dynamic proof,

Also all polygons make this theorem incorrect be careful.

## How do you find the missing side of a non right triangle?

First, use the law of cosines and plug in the values for the sides b,c and the angle A. second solve for side A, third use the angle value with the law of sines to find angle B. Finally, use the sum of the angles with the two angles to find angle C. You can find a missing angle by looking at the small triangle that includes angle B we now know that A=35 and, since the sum of the triangles equal 180 we can find angle B. Angle C and the 95 angle are supplementary; They add up to 180. Now we know C=85 we can find angle B since the three angle in the triangle add up to 180.

Step:1 Draw a right triangle and then read through the problems to determine the length of the legs and the hypotenuse.

Step:2 use the pythagorean theorem (a^2+b^2=c) to write an equation to be solved. Remember A and B are the legs and C is the hypotenuse.

Step:3 simplify the equation by distributing and combining like terms as needed.

Step:4 solve the equation, If the equation contains x^2, set the equation equal to zero and solve the equation by factoring. If the equation does not contain x^2 then solve the equation by getting the variables on one side and the numbers on the other side.

Step:5 answer the question asked in the original question and make sure that the answer makes sense don’t forget to include units in your answer.

## How do you know if the triangle is a right triangle?

If the square of the length of the longest side of the triangle is equal to the sum of the squares of the strengths of the other 2 sides, then the triangle is a right triangle. The variabies stands for the three side of a right triangle. A and B square are the legs that makes the triangle and C square is the hypotenuse.

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