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GCSE CCEA Pythagoras' theoremPythagoras' theorem is used to find the length of a side in a right-angled triangle. Part of Maths Geometry and measure
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Identifying right-angled triangles using Pythagoras' theoremIt is possible to determine if a triangle contains a right angle using Pythagoras' theorem. If the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle. ExampleDoes the triangle ABC contain a right angle? \[a^2 + b^2 = c^2\] \[5^2 + 6^2 = c^2\] \[61 = c^2\] The hypotenuse of the triangle is 8. \[8^2 = 64\] 61 does not equal 64. Therefore, the triangle does not contain a right angle. QuestionDoes the triangle PQR contain a right angle? \[a^2 + b^2 = c^2\] \[5^2 + 12^2 = c^2\] \[169 = c^2\] The hypotenuse of the triangle is 13. \[13^2 = 169\] 169 is equal to \(c^2\). Therefore, the triangle does contain a right angle.
GCSE Subjects
What is the formula for a right angle triangle?In a right triangle with cathetus a and b and with hypotenuse c , Pythagoras' theorem states that: a² + b² = c² . To solve for c , take the square root of both sides to get c = √(b²+a²) . This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".
How do you find an angle in a right triangle with two sides?Example. Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100).. Step 2 SOHCAHTOA tells us we must use Cosine.. Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333.. Step 4 Find the angle from your calculator using cos-1 of 0.8333:. |
How to find a right angle triangle
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