Δ ABC is right angles triangle with \(\angle\)B = 90°. If AB = 3\(\sqrt {3 }\)cm and \(\angle\)A = 30°, then find the value of AC - BC.

3cm

tan 30° = \(\frac{Perpendicular}{Base}\) = \(\frac{BC}{AB}\)

⇒ \(\frac{1}{\sqrt {3 }}\) = \(\frac{BC}{3\sqrt {3 }}\)

BC = 3cm

Also; cos 30° = \(\frac{base}{hypointense}\) = \(\frac{AB}{AC}\)

⇒ \(\frac{\sqrt { 3}}{2}\) = \(\frac{3\sqrt {3 }}{AC}\)

⇒ AC = 6cm

∴ AC - BC = (6-3)cm = 3cm