pythagorean theorem?

Question

why can the pythagorean theorem only be used with Right Triangles and what does it tell about a right triangle?

Answer 1

Well, if it bothers you that this theorem only works for right triangles, then just get familiar with the Law of Cosines: Given two sides a and b, and their interior angle α, then the third side c can be calculated by the formula

c² = a² + b² - 2ab * cos(α)

Note that, if you have a right triangle, then cos(α) = cos(90°) = 0, so this equation reduces to the Pythagorean Theorem.

Answer 2

Only if there is a right triangle does c^2 = a^2 + b^2.
Here c is the side opposite the right angle (also called the hypotenuse) and a and b ate the other twio sides of the triangle (also called the legs).

If c^2 > a^2+b^2 then the triangle will be obtuse, and if c^2 < a^2+b^2, the triangle will be acute.

The right triangle is the only triangle that has two of its sides that are altitudes of the triangle and hence its area is 1/2 the product of its two legs. Ittells us that certain right triangles are special such as the 30-60-90 rt triangle and the 45-45-90 rt triangle.

The right triangle has many features not enjoyed by non-right triangles. For example the altitude drawn from the vertex of the right angle to the hypotenuse forms two additional right triangles that are similar to eac other and to the original right triangle. From this fact, many additional properties can be derived.

I don't know if this answered your question, but it's time to stop rambling.

Answer 3

Because "right triangles" have a 90 degree angle. It is a special characterstic of triangles with a 90 degree angle. Most people know it as "a squared + b squared = c squared" where c is the hypotenuse or the side opposite the 90 degree angle. If "a squared + b squared < c squared" then you have an obtuse triangle where one angle is greater than 90 degrees. If "a squared + b squared > c squared" then the triangle is acute where all angles are less than 90 degrees.

There are many solutions to this: 3,4,5; 5,12,13; etc. But if you cubed a, b, and c (or even raised them to higher powers), can you prove that there are no whole number solutions? Andrew Wiles did!

Answer 4

pythagorean theorem can only be used with right triangles because that's the only situation in which it works... just like trig functions... it has something to do with ratios between the side lengths and angles but I don't know exactly...

pythagorean theorem is mainly used to find a missing side length, whether it be the hypotenuse or one of the legs.

a^2 + b^2 = c^2

c is hypotenuse

Answer 5

It says that if you add together the squares of the two sides adjacent to the right angle, they will equal the square of the other side. In other triangles the ratio varies depending on the angle.

Answer 6

To answer your question "why?", you must re-familiarize yourself with the proof of the theorem.
The proof is geometric.
It is, after all, a geometry problem - not an algebra problem, not a trig problem.
Most notably, a right triangle can be divided into two smaller triangles, both congruent to the original triangle.

Answer 7

The assertion of the theory grew to become into got here across on a Babylonian pill circa 1900-1600 B.C. whether Pythagoras (c.560-c.480 B.C.) or somebody else from his college grew to become into the 1st to discover its evidence won't be able to be claimed with any degree of credibility. Euclid's (c 3 hundred B.C.) aspects grant the 1st and, later, the favourite reference in Geometry.