In the given figure, AB = BD, BC = 20 cm and ∠D = 45°, the length of AC is :

1. 54.64 cm

2. 48.28 cm

3. 40 cm

4. 14.64 cm

We know that,

sin θ = $\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}$

From figure,

In △ BCD,

⇒ sin 45° = $\dfrac{BC}{BD}$

⇒ $\dfrac{1}{\sqrt{2}} = \dfrac{20}{BD}$

⇒ BD = $20\sqrt{2}$ m.

From figure,

⇒ AB = BD = $20\sqrt{2}$ m

⇒ AC = AB + BC = $20\sqrt{2} + 20$ = 28.28 + 20 = 48.28 cm.

Hence, Option 2 is the correct option.