Q: Why is a right angled triangle so named?

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I am guessing you mean a right angled triangle. The hypotenuse is the longest side on a right angled triangle. So it is the side facing / parallel to the right angle.

7, 8 & 12 are the sides of the triangle.And, for a right angled triangle the Pythagoras theorem is always applicable!Pythagoras theorem states that for a right angled triangle:(Longest Side)2 = (Side-1)2 + (Side-2)2(Longest side is called as the hypotenuse).So, using data in the question:If its a right angled triangle--->122 = 72 + 82i.e. 144 = 49 + 64 => 144 = 113, which is clearly not true!Hence, the triangle with the given sides is not a right triangle.

If you make one side the base the opposite vertex is the apex, so there are three possible apices.

If it is a right angled triangle it will conform to Pythagoras' Theorm: The square of the hypotenuse = the sum of the squares on the other two sides. The hypotenuse would be the longest side, so add the two shorter sides squared together and if this equals the longest side squared then the triangle is a right angle triangle.

You do not need to, if you have a right triangle that angle is 90* so the other 2 angles are 45* apiece. That is actually only partially accurate. There can be a right angled triangle with sides of 2-3-5. 5 being the hypotenuse in which the triangle's angles will not be 90-45-45 but 90-33.69-56.31. To find the angles of a right triangle, you will need to know the length of the sides. With the length of all three sides, you will need to utilize sine, cosine, and tangent to find the angles.

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I am guessing you mean a right angled triangle. The hypotenuse is the longest side on a right angled triangle. So it is the side facing / parallel to the right angle.

Yes, because you can notice that the right angled triangle has one right angle, so its only 1 perpendicular line. Hope this helped :D

Is 682 equal to 602 + 322 ? If so it's a right-angled triangle...

Perpendicular lines meet at a right angle so a right angled triangle has two lines which are perpendicular to eachother. However there are no parallel lines in a right angled triangle, or any triangles for that matter.

Does 742 = 242 + 702? If so, it is a right-angled triangle; if not, it isn't...

The third angle must be 90 degrees so it's a right-angled triangle

Add the squares of the two smaller sides. Is it equal to the square of the biggest side? If yes, it is a right angled triangle. 82 + 152 = 64 + 225 = 289 172 = 289 The same, so it is right angled.

An obtuse triangle or a right angle triangle. An equilateral is definitely an isoceles triangle * * * * * Not true. An obtuse or right angled triangles can be isosceles. It depends on the sizes of the two smaller angles. An isosceles triangle has two equal angles so a triangle with angles of size [A, (180-A)/2, (180-A)/2] degrees where 90 < A < 180 degrees would be an obtuse angled isosceles triangle. A triangle with angles of size (90, 45, 45) degrees is a right angled isosceles triangle.

7, 8 & 12 are the sides of the triangle.And, for a right angled triangle the Pythagoras theorem is always applicable!Pythagoras theorem states that for a right angled triangle:(Longest Side)2 = (Side-1)2 + (Side-2)2(Longest side is called as the hypotenuse).So, using data in the question:If its a right angled triangle--->122 = 72 + 82i.e. 144 = 49 + 64 => 144 = 113, which is clearly not true!Hence, the triangle with the given sides is not a right triangle.

The question is poorly specified, since the given triangle can be right angled at A or C. If it is right angled at A, then bc2 = ab2 + ac2 so that ab2 = 100 - 16 = 84 and ab = sqrt(84) = 9.165 Or it is right angled at C, and ab2 = bc2 + ca2 = 100 + 16 = 116 so that ab = sqrt(116) = 10.770

5" by 10" by 15" cannot be a right angled triangle because the square of the hypotenuse (longest side) must be equal to the sum of the squares of the other two sides.Proof:152 = 22552 + 102 = 25 + 100 = 125225 is not equal to 125 so the triangle is not a right angled triangle.All the others are right-angled triangles:92 + 122 = 152 [81 + 144 = 225]42 + 7.52 = 8.52 [16 + 56.25 = 72.25]1.52 + 22 = 2.52 [2.25 + 4 = 6.25]Answer9ft, 12ft, 15ft9² + 12² = 81 + 144= 225= 15²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.4cm, 7.5cm, 8.5cm4² + 7.5² = 16 + 56.25= 72.25= 8.5²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.5in, 10in, 15inThis one doesn't obey the triangle inequality, so it isn't a triangle at all. Anything that isn't a triangle isn't a right-angled triangle, and therefore we don't need to check it against Pythagoras' Theorem. But just to be thorough:5² + 10² = 25 + 100= 12515² = 225≠ 125Which disagrees with Pythagoras' Theorem, so this is not a right-angled triangle.1.5m, 2m, 2.5m1.5² + 2² = 2.25 + 4= 6.25= 2.5²Which agrees with Pythagoras' Theorem, so this is a right-angled triangle.

By Pythagoras's theorem, to make a right angled triangle, 142 + 152 should be 212 But 142 + 152 = 196 + 225 = 421 whereas 212 = 441 So these three sides cannot make a right angled triangle.