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°
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°