I study mathematics from time to time. Mathematics is a great tool for science and technologies. I guess nowadays Korean kids at grade three or four study trigonometry I want to have deeper understanding for practical applications.
Two sides and one opposite angle.
Triangle ABC given a = 5, A = 30 degrees, and b = 12
By the Laws of Sines,
sinB / b = sinA / a
sinB = b sinA / a
sinB = 12 sin30 / 5 = 1.2
sinB must be greater than equal to 1.
Thus, it’s an impossible triangle.
The book – Trigonometry by Michael Corral – on Example 2.3 of page 41 said so.
Technically even if the a is bigger than 6, in reality triangle can’t exist with only two sides. Many mathematicians live in delusional world which is completely separated from physical universe we are belong to.
This is one of main reasons why advanced mathematics is hard to study for average intelligent people like me. What matter worse is most scientists blindly believe in the physical universe must fit into established theories. Great road block against advancement of collective humanity.