Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.
First of all ... I'm not sure this will help, but let's stop and notice it anyway ... An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but an even number of odd numbers (like 1,3,5,7) add up to an even number. So if the sum is going to be exactly 400, then there will have to be an even number of items in the set.
Now, let's put down an even number of odd numbers to work with,and see what we can notice about them:
1, 3, 5, 7, 9, 11, 13, 15 .
Number of items in the set . . . 8 Sum of all the items in the set . . . 64
Hmmm. That's interesting. 64 happens to be the square of 8 . Do you think that might be all there is to it ?
An obtuse angle is one greater than 90 degrees, a right angle one that is 90, and acute less than 90.
An obtuse triangle is one with one obtuse angle, all the rest being acute. A right triangle is one with one right angle, all the rest acute. And finally, an acute triangle is one with three acute angles.
In this case, the angles measure 83 degrees, 31 degrees, and 66 degrees. All of them are acute angles, as they're all less than 90 degrees.
