Question

Please answer me x and my step correct please​

Answer 1

`x=4\sqrt6}`

Explanation:

Look at the picture.

ΔACD it's a triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

Therefore

CD : CB : DB = 1 : √3 : 2.

If BC = 16, then CD = 16 : 2 = 8 and CB = 8√3

ΔABC it's a triangle 45° - 45° - 90°. The sides are in ratio 1 : 1 : √2.

Therefore

AC : AB : CB = 1 : 1 : √2

If CB = 8√3, then AB = x = (8√3)/(√2)

`x=(8\sqrt3)/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)=(8\sqrt6)/(2)=4\sqrt6`

Answer 2

Answer:x=4√6

Explanation:

In ∆DCB, cos30°=BC/DB

√3/2*16=BC

BC=8√3

Applying PYTHAGORAS THEOREM in ∆BAC,

(8√3)^2=2x^2

x=4√6