Question

How did it get 683.8?

Answer 1

9514 1404 393

Explanation:

638.8 is the result of evaluating the expression ...

  $\dfrac{400}{\dfrac{1}{\tan^2{57^\circ}}+\dfrac{1}{\tan^2{68^\circ}}}\approx\dfrac{400}{\dfrac{1}{1.53986^2}+\dfrac{1}{2.47509^2}}=\dfrac{400}{0.42173+0.163237}\\\\\\=\dfrac{400}{0.584967}=683.799\approx\boxed{683.8}$

Any scientific or graphing calculator or spreadsheet can compute this for you. (You may need to be careful to set Degrees mode for the angles.)