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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. [7] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem. It states that the sum of the two legs squared equals the hypotenuse squared.
The three sides of a right triangle are related by the Pythagorean theorem, which in modern algebraic notation can be written a 2 + b 2 = c 2 , {\displaystyle a^{2}+b^{2}=c^{2},} where c {\displaystyle c} is the length of the hypotenuse (side opposite the right angle), and a {\displaystyle a} and b {\displaystyle b} are the lengths of the legs ...
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
This proof is independent of the Pythagorean theorem, insofar as it is based only on the right-triangle definition of cosine and obtains squared side lengths algebraically. Other proofs typically invoke the Pythagorean theorem explicitly, and are more geometric, treating a cos γ as a label for the length of a certain line segment. [12]
Draw an equilateral triangle ABC with side length 2 and with point D as the midpoint of segment BC. Draw an altitude line from A to D. Then ABD is a 30°–60°–90° triangle with hypotenuse of length 2, and base BD of length 1. The fact that the remaining leg AD has length √ 3 follows immediately from the Pythagorean theorem.
Daily average mortgage rates on popular terms are rising as of Friday, December 20, 2024, with sharp moves higher for 30-year terms edging closer to 6.90% — an average 20 basis points higher ...
This can be seen by applying the Pythagorean theorem to a right triangle with horizontal and vertical sides, having the line segment from to as its hypotenuse. The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the area of the square on the ...