Are the given lengths 24, 60, 66, sides of a right triangle?

No because 60+66+24 equal up to 150° and a right triangle or all triangles have to equal to 180° degrees and a right triangle has a 90° angle in this case it doesn't have one so technically the answer will be no

24+60=84>66

60+66=126>24

66+24=90>60

Therefore, the lengths are the sides of a triangle because the sum of lengths of two sides must be greater than the third side. All the sum of length of 2 sides are greater than the third side.