Question

Refer to the above figure and find the length of $AC$, if the area of triangle $ABC$ is $15$.

• A. $2.1$
• B. $4.1$
• C. $6.2$
• D. $8.2$
• E. $9.6$

Answer 1

The correct option is C $6.2$

By sine rule, we get $\frac{AC}{\sin 52}=\frac{CB}{\sin 38}$ , which implies $CB=0.7813AC$
Area of triangle is $\frac{1}{2}\times AC\times CB=0.39{AC}^2=15$
$\Rightarrow {AC}^2=38.46$
$\Rightarrow AC=6.2$