Question

If a triangle is a right triangle, then the other two angles must be acute

Answer 1

Yes this is true. Because since one of the angle in a triangle is a right angle ( 90degrees, the sum of the other 2 angles cannot exceed 90 also ( since 180 - 90= 90) Thus they must be acute.

Answer 2

i guess we are assuming the triangle in a plane

Answer 3

Hmm not really relevant to the question but may i ask UnkleRhaukus why must it come with the assumption that the triangle is lying in a plane. Does it matter?

Answer 4

@UnkleRhaukus - a triangle can exist only in a plane I guess :P

Answer 5

Triangles can also exist in a hyperbolic or elliptic geometry, in which case this statement would not be true. These are called non-Euclidean geometries. They are almost certainly not relevant to the question here.

Answer 6

I am sorry, I didn't understand that @nbouscal - Can you give an example?

Answer 7

Think of a triangle that goes from the north pole to two points on the equator of a globe. All three angles can be ninety degrees.

Answer 8

But we are talking about angles within a triangle, even those would obey the geometrical rule of all angles within a triangle to be equals to 180 degress, no?

Answer 9

surprisingly not

Answer 10

No, tiaph, this is the point I am making. The triangle on the surface of a globe with all three angles being 90 degrees is still a triangle.

Answer 11

The rule that a triangle's angles must sum to 90 degrees is only true in Euclidean geometry.

Answer 12

Okay now i get what you mean. Thanks ;D

Answer 13

Made a typo in my previous comment, wrote 90 when I meant 180.

Answer 14

But then, this triangle is formed by curves - so can it still be called a 'triangle'?

Thanks a million @nbouscal and @UnkleRhaukus - that helped a lot btw :)

Answer 15

Yep i imagined that scenerio but i was still thinking of how even though the triangle may lie on the surface, but the imposed triangle that can go through the surface and lie in the same plane, will still obey Euclidean geometry.

Answer 16

Yes, apoorvk, it is still a triangle. In the context of elliptical and hyperbolic geometries, the plane itself is curved. So, it isn't the lines that are curved, it is the plane itself. This is relevant to physics in the area of general relativity, by the way.