Triangles...?

Question

I don't understand it.

I'm looking at one of my problems and it shows a triangle that has three unequal (in legnth) sides. So that would be a scalene triangle... but it also has a 90º angle. But don't most triangles have that? I can't tell what a right angle is and what isn't.

Answer 1

right triangle can be scalene
if one of the angles is 90* it is a right triangle
if it is a right triangle the side opposite to the right angle is known as the hypotenuse say 'c'
and the other two sides the legs say 'a' and 'b'
the Pythagoras theorem states that c^2=a^2+b^2 in a right triangle

Answer 2

No, there is no requirement at all that any triangle have a 90º angle. In your textbook you simply see a lot of those because most of the early things you learn have to do with simple problems, not complex ones.

A right angle is that 90º angle you mention. A triangle with one (and there can't be two!) is called a "right triangle." Usually, when showing them in your textbook, you will see a little box drawn in the angle that is 90º though sometimes you will see a "90º" written in as the measure of the angle.

A triangle with a 90º angle CAN be scalene as well but does not have to be.
A scalene triangle CAN have a 90º angle as well but does not have to.

Answer 3

It's possible for a triangle to have three unequal sides and still have a right angle. Remember that if a triangle has three unequal sides, that means it has three unequal angles.

A right angle triangle with sides 3,4, and 5 is a scalene triangle. There are only three types of triangles in the same category: scalene, isoseles, equilateral. It's possible for a right angle triangle to be scalene and isoseles, but not equilateral.

Answer 4

Be prepared that most triangles do not have 90 degrees angle! Use cosine theorem c^2=a^2+b^2-2ab*cos(u) or cos(u)=(a^2+b^2-c^2)/(2ab), where u is the angle opposite to the side c, that is between a and b sides. If cos(u)=0, u=90degrees; if cos(u)>0, then u<90; if cos(u)<0, then u>90;
As an example consider Egyptian triangle with sides 3, 4, 5;

Answer 5

It's not true that most triangles have a 90 degree angle. And yes, having a 90 degree angle is the definition of a right-angled triangle.

Answer 6

you can have a scalene right triangle. In fact, most right triangles are scalene, and absolutely none of them are equilateral.

a 90 degree angle is a right angle. you're not wrong.