From the adjoining figure, find

(i) tan x°

(ii) x

(iii) cos x°

(iv) use sin x° to find y.

(i) By formula,

tan x° = $\dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AB}{BC} = \sqrt{3}$.

Hence, tan x° = $\sqrt{3}$.

(ii) tan x° = $\sqrt{3}$

⇒ tan x° = tan 60°

⇒ x = 60.

Hence, x = 60.

(iii) Substituting value of x in cos x°, we get :

⇒ cos x° = cos 60°

⇒ cos x° = $\dfrac{1}{2}$.

Hence, cos x° = $\dfrac{1}{2}$.

(iv) Substituting value of x in sin x°, we get :

⇒ sin x° = sin 60° = $\dfrac{\sqrt{3}}{2}$.

By formula,

$\Rightarrow \text{sin x}\degree = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}} \\[1em] \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{AB}{AC} \\[1em] \Rightarrow \dfrac{\sqrt{3}}{2} = \dfrac{\sqrt{3}}{y} \\[1em] \Rightarrow y = 2.$

Hence, y = 2.