In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if :

(i) AB is ${\sqrt3}$ times of BC.

(ii) BC is ${\sqrt3}$ times of AB.

(i) AB = ${\sqrt3}$ BC

$\dfrac{AB}{BC} = \sqrt3$

$\text{cot θ} = \dfrac{AB}{BC}\\[1em] \text{cot θ} = \sqrt3\\[1em] \text{cot θ} = \text{cot 30°}\\[1em]$

So, θ = 30°

Hence, magnitude of angle A = 30°.

(ii) BC = ${\sqrt3}$ AB

$\dfrac{BC}{AB} = \sqrt3$

$\text{tan θ} = \dfrac{BC}{AB}\\[1em] \text{tan θ} = \sqrt3\\[1em] \text{tan θ} = \text{tan 60°}\\[1em]$

So, θ = 60°

Hence, magnitude of angle A = 60°.