Description for the calculation of right triangles and the Pythagorean theorem
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. The hypotenuse is the longest side of a right triangle. It is always across from the right angle.
sed on this right triangle, you can write an equation using the Pythagorean Theorem as follows
\(a^2+b^2=c^2\)
\(\sqrt{s^2+b^2}\)
A Pythagorean triplet is made up of three natural numbers, which may appear as lengths of the sides of a right triangle.
A Pythagorean triple is a right triangle whose sides are in the ratio 3:4:5
The side lengths do not need to measure 3, 4, and 5; however, they do need to reduce to that ratio
For example, the side lengths 9, 12, and 15 are a Pythagorean triple because it simplifies to the ratio 3:4:5
You can also use the Pythagorean Theorem to determine if a triangle is acute, right, or obtuse. This is known as the converse of the Pythagorean Theorem, which reads as follows
wo types of right triangles are considered special right triangles. One of the special right triangles has angles that measure 30°, 60°, and 90°. The other special right triangle has angles that measure 45°, 45°, and 90°. The size of the triangle does not matter; it just needs to have specific measures for its angles.
The lengths of the sides of a \(30° - 60° - 90°\) triangle are in a ratio of \(b=a·\sqrt{3}\)
The hypotenuse is twice the length of the side \(a\) opposite the \(30°\) angle.
Using this information, you can determine the value of \(a\) and \(b\) for the triangle, if you know the value of \(c\).
The sides \(a\) of a 45° - 45° - 90° triangle are the same length.
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