ΔABC is right angled at B. If ∠A = 30°, what is the length of AB (in cm), if AC = 10 cm?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given,}} \cr & \angle A = {30^ \circ } \cr & \therefore \angle C = {60^ \circ } \cr & \left( {\tan {{60}^ \circ } = \frac{{\sqrt 3 }}{1} = \frac{{AB}}{{BC}}} \right) \cr & AB = \sqrt 3 ,\,BC = 1 \cr & \therefore AC = \sqrt {A{B^2} + B{C^2}} \cr & = \sqrt {\left( {{{\left( {\sqrt 3 } \right)}^2} + {{\left( 1 \right)}^2}} \right)} \cr & = 2\,{\text{unit}} \cr & 2\,{\text{unit}} = 10\,{\text{cm}} \cr & 1\,{\text{unit}} = 5{\text{ cm}} \cr & \boxed{AB = \sqrt 3 {\text{ unit}} = 5\sqrt 3 } \cr} $$