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   ?

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

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

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