Find 'x' in each of the following

(i)

(ii)

(iii)

(i) The formula for tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

⇒ tan 30° = $\dfrac{\text{x}}{120}$

$\Rightarrow \dfrac{1}{\sqrt{3}} = \dfrac{\text{x}}{120}\\[1em] \Rightarrow \text{x} = \dfrac{120}{\sqrt{3}}\\[1em] \Rightarrow \text{x} = \dfrac{120 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}\\[1em] \Rightarrow \text{x} = \dfrac{120\sqrt{3}}{3}\\[1em] \Rightarrow \text{x} = 40\sqrt{3}$

⇒ x = 69.28 m

Hence, the value of x = 69.28 m.

(ii) The formula for tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

⇒ tan 45° = $\dfrac{\text{x}}{40}$

$\Rightarrow 1 = \dfrac{\text{x}}{40}$

⇒ 40 = x

Hence, the value of x = 40 m.

(iii) The formula for cos A = $\dfrac{\text{Base}}{\text{Hypotenuse}}$

⇒ cos x = $\dfrac{50}{100}$

⇒ cos x = $\dfrac{1}{2}$

⇒ cos x = cos 60°

⇒ x = 60°

Hence, the value of x = 60°.