what is the uses of Pythagoras theorem?

Answer 1

What everyone seems to be forgetting here is that there is a CONSTRAINT to Pythagorean theorem: the triangle has to be a right triangle. It may be the foundation upon which most of the geometric principles are based.

Answer 2

the Pythagorean theorem (AmE) or Pythagoras' theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[1] although knowledge of the theorem almost certainly predates him. The first recorded use is in China, known as the "Gougu theorem" (勾股定理).


The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).The theorem is as follows:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

This is usually summarized as:

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

If we let c be the length of the hypotenuse and a and b be the lengths of the other two sides, the theorem can be expressed as the equation


or, solved for c:


This equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. A generalization of this theorem is the law of cosines, which allows the computation of the length of the third side of any triangle, given the lengths of two sides and the size of the angle between them. If the angle between the sides is a right angle it reduces to the Pythagorean theorem.

Answer 3

Given: Figure - rectangular room Length, L = 5 m Width, W = 5 cm (?) Height, h = 2.5 m Required: Measurement of the diagonal Solution: Step1: Draw the figure and label it with the given data. You can discover that the room is a parallelogram in shape. Step2: Draw the diagonal of the parallelogram and label it with "c". Step3: You also draw the diagonal of the base area (diagonal of 5m * 5 cm?). If this is 5m x 5m, then, its a square base room. Step4: Now, you can already visualize that a right triangle formed by diagonal of the room, c; the diagonal of the base area, d; and the height of the room. Step5: Compute 1st for the diagonal of the base d, (I would assume that the width W = 5m). Using the Pythagorean Theorem which is; d^2 = L^2 + W^2 d^2 = (5m)^2 + 5m)^2 d^2 = 25 m^2 + 25 m^2 d^2 = 50 sq m d = √50 m^2 = √25 * 2 m^2 d = 5√2 m. ---------------------->>> measurement of the diagonal of base area (1) Step6: you can now proceed to the computation of the diagonal of the room because you have found d = 5√2 m and height h is given as = 2.5 m Using again the Pythagorean Theorem; c^2 = d^2 + h^2 c^2 = (5√2 m)^2 + (2.5m)^2 c^2 = 50 m^2 + 6.25 m^2 c^2 = 56.25 m^2 c = √56.25 m^2 c = 7.5 m ------->>> This is the diagonal of the room when width W = 5m. <<<>>> if width W = 5cm = 0. 05m (1m = 100cm) d^2 = (5m)^2 + (0.05m)^2 d^2 = 25.0025 m^2 going back to c^2 = d^2 + h^2 c^2 = 25.0025 m^2 + (2.5m)^2 c^2 = 31.2525 m^2 c = √31.2525m^2 c = 5.59 m ---> say 5.60 m In either way, your answer do not coincide with mine. maybe you shoud try to analyse again the problem... maybe if you use W = 3m, our answers will be the same .... :-)

Answer 4

3 (squared) + 4 (squared) = 5 (squared) or 9 + 16 = 25.

Therefore, you can knot a rope at lengths of 3, 4 and 5 units (one knot per foot, yard, meter or stick(?), etc.) and form a right triangle. This could be used as a quick way to lay out a 'square' corner for walls of a building or a fence, etc.

You can also use Pythagoras theorem to calculate the length of a diagonal of any square or rectangle (room, etc.) given the lengths of adjacent sides.

Answer 5

pythagoras theoram is used to find out the length of a side of a right angled triangle when 2 of the sides are given.square of hypotenuse of that triangle is equal to the sum of the square of 2 other sides.
a*a(hypotenuse)=b*b(any of the other sides)+c*c

Answer 6

pythagoras theoram is used to find out the length of a side of a right angled triangle when 2 of the sides are given.square of hypotenuse of that triangle is equal to the sum of the square of 2 other sides.
a*a(hypotenuse)=b*b(any of the other sides)+c*c

Answer 7

pythagorean theorem is used to find out the length of the side of a triangle when 2 of the sides are known. the equation is a squared plus b squared equals c squared, where a and b are the known side lengths, and c is the length you are looking for.

Answer 8

Phythagoras theorem is used to find the hypotenious of a tringle or the base or the other side of the tringle.
It is very useful because u can easily find the length of the other side without measuring.


{Hypotenious]squre = [base]squere + [opposite]squere

Answer 9

You can work out the distance for many things...as long as it involves a right angled triangle....and you know two sides..... Uhm.....Working out the third side of the triangle?

Answer 10

When objects are small enough to where it is more efficient to measure sides than angles. If the opposite is true use you sine and cosine.