Using the given figure, find the value of angle A, if :

(i) x = y

(ii) x = $\sqrt3$ y

(iii) $\sqrt3$ x = y

(i) Given: x = y

tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

= $\dfrac{x}{y}$

= $\dfrac{x}{x}$

= 1

⇒ tan A = tan 45°

⇒ A = 45°

Hence, the value of A = 45°.

(ii) Given: x = $\sqrt3$ y

tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

= $\dfrac{x}{y}$

= $\dfrac{y\sqrt{3}}{y}$

= $\sqrt{3}$

= tan 60°

⇒ tan A = tan 60°

⇒ A = 60°

Hence, the value of A = 60°.

(iii) Given: $\sqrt3$ x = y

tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

= $\dfrac{x}{y}$

= $\dfrac{x}{\sqrt{3}x}$

= $\dfrac{1}{\sqrt{3}}$

= tan 30°

⇒ tan A = tan 30°

⇒ A = 30°

Hence, the value of A = 30°.