[m]S_{ Δ ABC}=\frac{CH\cdot AB}{2}[/m]
⇒ [m]\frac{AC\cdot BC}{2}=\frac{CH\cdot AB}{2}[/m] ⇒
[m]AC\cdot BC=CH\cdot AB[/m]
[m]tg ∠ A=\frac{BC}{AC}[/m] ⇒ [m]AC=\frac{BC}{tg ∠ A}=\frac{7}{\frac{33}{4\sqrt{33}}}=\frac{28}{\sqrt{33}}[/m]
[m]AB^2=AC^2+BC^2[/m]
[m]AB^2=(\frac{28}{\sqrt{33}})^2+7^2=\frac{784}{33}+49=\frac{784+49\cdot 33}{33}=\frac{2401}{33}[/m]
[m]AB=\frac{49}{\sqrt{33}}[/m]
[m]\frac{28}{\sqrt{33}}\cdot 7=CH\cdot \frac{49}{\sqrt{33}}[/m]
[m]CH=\frac{33}{28}[/m]