From the information given in the triangle shown below, the length of CD is :

(take ${\sqrt3}$ = 1.732)

(i) 7.32 m

(ii) 27.32 m

(iii) 10 m

(iv) 17.32 m

In Δ ABD,

$\text{tan 45°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ 1 = \dfrac{AB}{BD}\\[1em] ⇒ 1 = \dfrac{10}{BD}\\[1em] ⇒ BD = 10 m$

In Δ ABC,

$\text{tan 30°} = \dfrac{Perpendicular}{Base}\\[1em] ⇒ \dfrac{1}{\sqrt3} = \dfrac{AB}{BC}\\[1em] ⇒ \dfrac{1}{1.732} = \dfrac{10}{BC}\\[1em] ⇒ BC = 10 \times 1.732 m\\[1em] ⇒ BC = 17.32 m$

As, BC = BD + CD

⇒ 17.32 = 10 + CD

⇒ CD = 17.32 - 10

⇒ CD = 7.32

Hence, option 1 is the correct option.