Question

Can someone help me on this question?

Answer 1

Answer:

x = 19.6

Step-by-step explanation:

By applying cosine rule in ΔBCD,

cos(30)° = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

              = $\frac{BC}{BD}$

$\frac{\sqrt{3}}{2}=\frac{BC}{16}$

BC = $8\sqrt{3}$

Now, by applying sine rule in ΔBAC,

sin(45)° = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{\sqrt{2}}=\frac{AB}{BC}$

$\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}$

x = $8\sqrt{6}$

x = 19.59

x ≈ 19.6