In trigonometry how would you know which angle will be hypotenious , base , and perpendicular in obtuse, right, and acute triangles?me to understand it properly

Hi there,
I'll try my best to explain this topic to you clearly.
So...
We know that a hypotenuse, right angle, etc. are all part of a right triangle.
(A picture of a right triangle is attached)
The square in the picture is basically the right angle, or the angle that measures 90°. This shows us that side a and side b are perpendicular, as the definition of perpendicular lines implies.

The hypotenuse, or the longest side in a right triangle, is the side opposite to the right angle. In this case, side c would be the hypotenuse of the right triangle. How do we know this? Well, side c is opposite to the right angle, making it the hypotenuse. 

There are no obtuse angles in a right triangle, which is because of the sum of angles in a triangle, 180°. So, if we tried for instance, to say that another angle apart from the right angle is 91°, then 91° + 90°(the right angle) is 181°, which is higher than the required value for the sum of angles in any triangle. 

The two other angles other than the right angle are obviously acute angles, as we learned from the previous paragraph. They can be ranging anything from 0 < x < 90. This inequality helps a lot if you are still trying to see if an angle is acute or right. 
Hopefully, I answered your question and explained this topic to you very well. If you need more help, just DM me and I'll explain it to you more. Have a splendid day!

The answer would be $68.04