Compute the Area of Triangle ABC

Question

In $\Delta ABC , m \angle A=30$.$BC^2 = 16 (10-3\sqrt3)$ .
$AC:AB = 1:3$.
Compute the area of $\Delta ABC$

Answer 1

Hints:

1. Use the cosine rule to find $BC^2$.

2. Substitute $AB=3AC$ into the equation to find $AC$, then $AB$.

3. The area is: $S=\frac12\cdot AC\cdot AB\cdot \sin30^\circ$.