Trigonometry help

What does a² = 58 - 42 cos 35   ?

$$\\ a^2 = 58 - 42 \cos{( 35 \ensurement{^{\circ}} )} \\
a^2 = 58 - 42 * 0.81915204429 \\
a^2 = 23.5956141399 \quad | \quad \sqrt{}\\
a = 4.85753169211$$

What does a² = 58 - 42 cos 35   ?

$$\begin{array}{ccccl}
a^2 &=& b^2+c^2 & -2bc & *\cos{ ( \alpha ) }\\
a^2 &=& 58 &-42 & *\cos{ ( 35\ensurement{^{\circ}} ) }
\end{array}$$

$$\\ \small{\text{
(1)
}}
\ b^2+c^2 = 58
\\
\small{\text{
(2)
}}
\ 2bc = 42 \small{\text{ or }} c = \frac{21}{b}$$

$$\small{\text{
(2) in (1):
}}
\ b^2 + \frac{(21^2)} {b^2} = 58 \small{\text{ or }} b^4-58b^2+21^2=0 \\ \small{\text{ if }} x=b^2 \small{\text{ then }} x^2-58x+21^2=0 \\
x_{1,2} = \frac{58\pm40}{2} \small{\text{ so }} x_1=49 \small{\text{ and }} x_2 = 9 \small{\text{ because }} b=+\sqrt{x} \\
\small{\text{ so }} b_1 = 7 \small{\text{ or }} b_2 = 3 \\
c=\frac{21}{b} \small{\text{ so }} c_1 = 3 \small{\text{ or }} c_2 = 7$$