Triangle question

By the Pythagorean Theorem,

35² + ( CB )²  =  50²

                                         Subtract  35²  from both sides of the equation.

( CB )²  =  50² - 35²

                                         Simplify the right side of the equation.

( CB )²  =  1275

                                         Since  CB  is a length, take the positive square root of both sides.

CB  =  √[ 1275 ]

                                         And we can simplify the radical.

CB  =  5√[ 51 ]

                                         To get an approximate solution, plug it into a calculator.

CB  ≈  35.707

sin( angle )  =  opposite / hypotenuse

sin( C )  =  35 / 50

                                         Take the inverse sine of both sides of the equation.

C  =  arcsin( 35 / 50 )

                                         Plug  arcsin(35/50)  into a calculator to get...

C  ≈  44.427°