Exploring The Properties And Applications Of The 3-4-5 Triangle: A Special Right Triangle With Versatile Applications In Geometry

3-4-5 triangle

a triangle in which the sides are 3, 4, and 5 units long. A 3-4-5 triangle is always a right triangle.

The 3-4-5 triangle is a right triangle, which means one of its angles is a right angle (90 degrees) and its other two angles are acute (less than 90 degrees). The sides of the 3-4-5 triangle are in a ratio of 3:4:5, which means that the length of the shortest side (opposite the smallest angle) is 3 units, the length of the middle side (opposite the middle angle) is 4 units, and the length of the longest side (opposite the right angle) is 5 units.

There are several properties of the 3-4-5 triangle that make it useful in various applications. For example:

– The 3-4-5 triangle is one of the Pythagorean triples, which means that its sides satisfy the Pythagorean theorem (a^2 + b^2 = c^2). In this case, 3^2 + 4^2 = 5^2, which verifies that the 3-4-5 triangle is indeed a right triangle.

– The 3-4-5 triangle can be used to find the lengths of other right triangles that are similar to it. For example, if you have a right triangle with a leg that is twice as long as the corresponding leg of a 3-4-5 triangle, then the other leg will be twice as long as the corresponding leg of the 3-4-5 triangle, and the hypotenuse will be twice as long as the corresponding hypotenuse of the 3-4-5 triangle.

– The 3-4-5 triangle can be used to construct other geometric shapes, such as squares and rectangles. For example, if you draw a square with sides of length 3 units, and then draw a diagonal (which will have length 5 units), you will create a right triangle that is similar to the 3-4-5 triangle.

In summary, the 3-4-5 triangle is a special right triangle that has useful properties in various applications. Its sides are in a ratio of 3:4:5, which makes it easy to work with and apply to other geometric shapes.

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