Then the students should
No because a scalene triangle has no right angles
No. In an equilateral triangle, all three angles are the same. Since they are not ninety degrees, you can't have a right triangle that is also an equilateral triangle.
Yes with the help of a protactor remembering that the triangle will have 1 obtuse angle and 2 different acute angles with 3 sides of differerent lengths. The 3 interior angles must add up to 180 degrees.
Equilateral means 'equal length' and defines a specific size of triangle with equal interior angles Equiangular means only that the interior angles are equal, but the sides could be of anylength, even infinite! (very tricky to sketch!!!)
Yes it is possible
OK. Done. Now what ?
No, I can't. No such thing can exist. -- The interior angles of every triangle add up to 180 degrees. -- An obtuse triangle is one with an angle greater than 90 degrees in it. -- An equiangular triangle is one with all 3 angles the same size. If one of them is obtuse, then they're all obtuse. -- Three times (more than 90 degrees) = (more than 270 degrees). Not possible. -- So an obtuse equiangular triangle can't exist.
A triangle.
no; a triangle must have an obtuse angle if one of its altitudes is outside of the triangle, and in this case 2 of the altitudes are out of the triangle.
All equilateral triangles are cute.
Yes, but not on this site. All triangles must have at least two acute angles. Take one of these and the exterior angle associated with it will meet your requirements.
Make a sketch of the situation. From a corner of the equilateral triangle draw a radius of the large circle, and from an adjacent side draw a radius of the smaller circle. You should have formed a small right-angled triangle with a known side of 10cm. and known angles of 30o, 60o and 90o. (The interior angles of an equilateral triangle are each 60o.) The hypotenuse is the unknown radius of the larger circle. But since cos 60 = 0.5, it is evident that the hypotenuse is 20cm. long.