In △ ABC, ∠B = 90°, AB = y units, BC = ${\sqrt3}$ units, AC = 2 units and angle A = x°, find :

(i) sin x°

(ii) x°

(iii) tan x°

(iv) use cos x° to find the value of y.

(i) sin x° = $\dfrac{Perpendicular}{Hypotenuse}$

= $\dfrac{BC}{AC} = \dfrac{\sqrt3}{2}$

Hence, sin x° = $\dfrac{\sqrt3}{2}$.

(ii) x°

sin x° = $\dfrac{\sqrt3}{2}$

⇒ sin x° = sin 60°

Hence, x = 60°.

(iii) tan x° = tan 60°

tan 60° = $\sqrt3$

Hence, tan 60° = $\sqrt3$.

(iv) cos x° = $\dfrac{Base}{Hypotenuse}$

= $\dfrac{AB}{AC} = \dfrac{y}{2}$

cos x° = cos 60° = $\dfrac{1}{2}$

So, $\dfrac{y}{2} = \dfrac{1}{2}$

⇒ y = 1

Hence, y = 1.