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Does the Pythagorean Theorem work on all triangles with side length of 1?
It doesn't matter on the side length, but it MUST have a right angle.
What is the altitude of a equilateral triangle if one side is 6 cm?
An equilateral triangle has all 3 sides the same length. To find the height of a triangle, draw a line from the tip top of the triangle to the middle of the base. You should see 2 triangles now inside your original triangle. We can use Pythagoras' theorem to figure out the length of this line, the height. This theorem will only work with right triangles, which (luckily) we have just created by drawing the height line inside the triangle. The P. theorem says that side squared + side squared = hypotenuse squared. Our hypotenuse is the left or right side of the original triangle, 6 cm. The line we drew down the center is one side, and HALF of the base is the other side for the P. theorem, since the height line of the triangle cuts the base exactly in half, and creates 2 right angles at the base. This line also creates 2 right triangles inside. This is why we can use the P. theorem to help us! But we'll only be using 1 of the inside triangles. (Even though, both are identical) side squared + side squared = hyp. squared (3 cm) squared + ??? squared = 6 squared 9 + ??? squared = 36 ??? squared = 36 - 9 ??? squared = 27 ??? = sqrt(27) We can simplify sqrt(27), or you can use a calculator to approximate it. sqrt(27) = sqrt(9*3) = 3 * sqrt(3)
Does 2 equilateral triangles make a square?
No, two equilateral triangles do not make a square. A square has four equal sides and four right angles, while an equilateral triangle has three equal sides but three angles that add up to 180 degrees. When two equilateral triangles are put together, they do not form a shape with four equal sides and four right angles, which is the defining characteristic of a square.
Does the Pythagorean theorem work with Euclidean and Hyperbolic geometry?
It works in Euclidean geometry, but not in hyperbolic.
How can a lawyer use Pythagorean Theorem?
If needed, I guess. I do not see lawyers needing the Pythagorean Theory in their work and lawyers are notoriously ignorant of math and science.
