Explain why a pythagorean triple can represent the measure of the sides of a right triangle.?
396361
Pythagorean triples are integer length sides of right triangles.\n\nIts in the form of (t^2 - s^2, 2st, t^2 + s^2)\n\nusing that can create another right triangle.\n\nSorry, but thats about all i could dig up. I'm not really all that familiar with P.T.
722679
60\n\nThe Babylonian sexagesimal number system, all Pythagorean triples have the property that the product of the 3 sides is a multiple of 60. I lived at a house which was no 60 in its street. And I am now 60.
117735
Use the Pythagorean theorem (twice).  The ray from the top light to the observer's eye is a straight line that just grazes the surface of the earth.  One right triangle has the following 3 sides: center of earth (COE) to surface (a known quantity), COE to top light (also known) and distance from tower to graze point (unknown).  The right angle is at the graze point.  Set up the other triangle similarly for the observer's eye, solve for the 2 unknowns, then sum them.
1115391
I think your teacher is looking for choice b., but technically it's choice a., because any triangle can be split into right triangles by drawing appropriate altitudes and then using the theorem for those smaller right triangles.
195780
In any right triangle, the area of the square whose side is the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.\n\na^2 + b^2 = c^2
726104
Pythagoras (of Samos, born about 569-82 BC - died about 507 BC) was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. \n\nIn any right triangle, the area of the square whose side is the hypotenuse (the long side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse, the adjacent and opposite in sine, cosine and tangent workings). \n\nIf 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\n\nThis 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.\n\nI was taught this in a long jumpo sand pit, with 25 billard balls.\nmy old teacher, Mr Chadwick, made a line of 5 balls, and this was the hypotenuse. he then drew in the rest of the triangle. he squared the 5 balls, by making a square of 5 by 5 balls, (25 in all).\n\nthen he put balls on the other lines. three fitted onto the short side, and four onto the next side. he then squared the two other sides. 3 x3 and 4 x 4 (9 and 16, when added together = 25. \n\nhe showed me that 27 years ago, It was amazing, and the reason I am now a teacher.
892974
a right triangle is called a right triangle because there is a 90 degree angle in it.
87753
Just add up the lengths of the three sides. Works for any triangle - wether it's equilateral, isosceles or obtuse.
585284
I think you mean he discovered that the angles in a triangle add up to the sum of two right angles (180 degrees). However, he is best known for the Pythagorean Theorem, which says that for all right triangles the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Many mathematicians and others, including President Garfield, have come up with original proofs for this theorem. Here's a couple links, one to information about the famous theorem and another to biographical information on Pythagoras.
71806
In an isosceles right triangle, sides a and b are equal and c is the hypotenuse.  Pythagorean's Theorum says that a^2 plus b^2 = c^2 for all right triangles.  here, a and b are equal, so you can say 2(a^2)=c^2.  If you want to solve for c, you find that c = a(rad2)
1116580
Brian gave you the answer, but he didn't explain it thoroughly.\n\nPlace your vector at the origin of an x and y plane.  The x and y axes are perpendicular, so you can use the Pythagorean formula to get the magnitude which is the length of the hypotenuse of the right triangle formed by the points (0,0), (10,0), and (0,8). sqrt(10^2+8^2)\n\nNow you need direction which is the angle between the x axis and the vector. Since you have solved for all three lengths of the triangles sides, you can use any inverse trig function to find the angle.  Brian chose tangent.\n\nGood work, Brian!
545074
The word "Trigonometry" is derived from two Greek words meaning measurement or solution of triangles. Trigonometry is a branch of mathematics that deals with the ratio between the sides of a right triangle and its angles. Trigonometry is used in surveying to determine heights and distances, in navigation to determine location and distances, and in fields like nondestructive testing for determining things such as the angle for reflection or refraction of an ultrasound wave.\n\nThere are three principle functions in trigonometry: sine A, cosine A, and tangent A where A is an angle. These are typically abbreviated for use in algebra to: sinA, cosA, and tanA. These terms are defined in terms of a right triangle. SinA is equal to the side opposite of the angle A (side a) divided by the hypotenuse of the triangle (side c). From the right triangle below, it can be seen that the value of angle A is directly linked to the ratio of side a and side c. In other words, if the length of side a is changed (and side c is not changed by the same amount), then angle A must change. When the division of the length of side a by side c is performed, the resulting value is directly related to angle A. The relationship between the decimal value of the ratio of the side and the angular value of angle A can be looked up in trigonometry tables or, as is more common these days, programmed into a scientific calculator. The relationship between angle A and the ratio of any two of the three sides can be determined by using either the Sin, Cos or Tan functions. CosA is equal to the side adjacent to the angle A divided by the hypotenuse and tanA is the sine divided by the cosine and is therefore the side opposite the angle divided by the side adjacent.
876350
Sorry, but your question doesn't make sense.  Maybe you mean the midpoint of one of the sides of a right triangle.
352939
it should have a right angle.\n\nThus, it's a right triangle
45454
Do you mean the Pythagorean theorem?\n\nIn any right triangle, the area of the square whose side is the hypotenuse (the side of the triangle opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.
352673
Make right triangles with the height as one leg, a radius (segment from center of base to one of its vertices) as the other leg, and lateral edge as the hypotenuse.  The radius will equal the length of the base edge as it's a side of an equilateral triangle.  So 10^2 + 15^2 will equal lateral edge squared.\n\nSlant height would be the hypotenuse of a right triangle with legs of the pyramid's height, and the apothem (distance from center of base to midpoint of a side.)  You can get the apothem from Pythagorean theorem from the right triangle formed by half a base edge, a radius, and the apothem.  Then use the apothem in another Pythagorean theorem to get slant height.\n\nLateral area = 6 times the area of any one triangle.  Each triangle's area is 1/2 times 10 times slant height.\n\nVolume = 1/3 (area of base)(height).  The area of the base is 1/2 (apothem)(perimeter).\n\nThose are the steps.  Hope you can figure them out from this typing!
394622
A triangle in which all 3 sides are of different lenghts, with different angles.