Word problem II

Helen solved a physics assignment:

Two forces act on the mass point $A$. The force $\overrightarrow{F_1}$ has a magnitude of $2\,\mathrm{N}$. The force $\overrightarrow{F_2}$ has a magnitude of $6\sqrt2\,\mathrm{N}$ and forms an angle of $45^\circ$ with $\overrightarrow{F_1}$. Determine the magnitude of their resultant force $\overrightarrow{F}$ and the angle $\alpha$ that $\overrightarrow{F}$ forms with $\overrightarrow{F_1}$.

Here is the Helen’s solution:

(1) Helen drew the vectors $\overrightarrow{F_1}$, $\overrightarrow{F_2}$, and $\overrightarrow{F}$ in the Gauss plane and labeled the complex numbers corresponding to the endpoints of these vectors as $f_1$, $f_2$ and $f$.

(2) Next, Helen expressed the complex numbers $f_1$ and $f_2$ in polar form: \begin{aligned} f_1&=2\left(\cos⁡0^\circ+\mathrm{i}\sin⁡0^\circ\right)\cr f_2&=6\sqrt2\left(\cos⁡45^\circ+\mathrm{i}\sin⁡45^\circ\right) \end{aligned}

(3) Then, she expressed $f_1$ and $f_2$ in algebraic form: \begin{aligned} f_1&=2\cr f_2&=6+6\mathrm{i} \end{aligned}

(4) She stated that $f$ is the sum of $f_1$ and $f_2$ and determined the magnitude $|f|$ of $f$: \begin{aligned} f&=8+6\mathrm{i}\cr |f|&=10 \end{aligned}

(5) Helen determined the argument $\alpha$ of $f$ as a solution of the following system of equations: $$\sin⁡\alpha=\frac35 \land\cos⁡\alpha=\frac45$$ $$\alpha\approx36^\circ87^{'}$$ (6) Finally, Helen wrote down the result of the task: The magnitude of the resultant force $\overrightarrow{F}$ is $10\,\mathrm{N}$ and the angle that $\overrightarrow{F}$ forms with $\overrightarrow{F_1}$ is $36^\circ 87^{'}$.

In which step of her solution did Helen make a mistake?