Determine the unknown angle...
This problem has been proposed by David Orlando Blanco (A.K.A. White's) to determine how skillful are you at math. The solution is done by recognizing that the angles inside this triangle are independent from its size. Analytic demonstration is done by assuming the triangle base () as 1.
Here's the graphic demostration...
Thanks White's for screwing my holiday with this problem :)
But in serious terms, it provides a funny way to remember the use of cosine and sine laws.
Algebraic demostration
Assuming the base b = 1, we can set the following relations. By Sine Law on the base triangle ACE:
Now on the triangle AED:
Now on the triangle BEC:
Now, using cosine law on triangle BDE:
We replace the letters with the proper values:
, , and
And, at last, determining the value of we can now determine the angle required using the Sine Law:
In order to test the result, I suggest to avoid rounding the values in the calculator, mainly in the calculation. Thanks for reading.