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GCSE OCR Pythagoras' theoremPythagoras’ theorem can be used to calculate the length of any side in a right-angled triangle. Pythagoras’ theorem can be applied to solve 3-dimensional problems. Part of Maths Geometry and measure
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Calculating the length of one of the shorter sidesRearrange Pythagoras' theorem to calculate the length of one of the shorter sides. \(a^2 + b^2 = c^2\) calculates the length of the longest side. To calculate the length of one of the shorter sides, rearrange the formula to make \(a^2\) or \(b^2\) the subject. \(a^2 = c^2 - b^2\) or \(b^2 = c^2 - a^2\) Then take the square root to calculate the length \(a\) or \(b\). ExampleCalculate the length AB. \[a^2 + b^2 = c^2\] \[8^2 + b^2 = 10^2\] Rearrange the formula to make \(b^2\) the subject: \[b^2 = 10^2 - 8^2\] \[b^2 = 36\] \[b = \sqrt{36}\] \[b = 6~\text{cm}\] The length AB is 6 cm. QuestionCalculate the length AO. Give the answer to one decimal place. \[a^2 + b^2 = c^2\] \[3^2 + b^2 = (\sqrt{17})^2\] Rearrange the formula to make \(b^2\) the subject. \[b^2 = (\sqrt{17})^2 - 3^2\] \[b^2 = 17 - 9\] \[b^2 = 8\] \[b = \sqrt{8}\] \[b = 2.8~\text{cm}\] The length AO is 2.8 cm.
GCSE Subjects
What is the shortest side of a triangle?The shortest side of a triangle is always opposite the smallest angle. For example, in ∆ABC below, side BC is the shortest side and is opposite angle A.
What is the 3 4 5 Triangle rule?The 3:4:5 triangle is the best way I know to determine with absolutely certainty that an angle is 90 degrees. This rule says that if one side of a triangle measures 3 and the adjacent side measures 4, then the diagonal between those two points must measure 5 in order for it to be a right triangle.
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What is the shorter side in a triangle?
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