Question

Given an acute $△ABC$ such that $\sin C=\frac{4}{5}$, $\tan A=\frac{24}{7}$ and $AB=50$. The area of the $△ABC$.

• A. $600$
• B. $1200$
• C. $1800$
• D. $2400$

Answer 1

The correct option is B $1200$

$\sin C=\frac{4}{5},\tan A=\frac{24}{7}⟹\sin A=\frac{24}{25}$

$\frac{a}{\sin A}=\frac{c}{\sin C}⟹a=50\times \frac{24}{25}\times \frac{5}{4}=60$

$\Delta =\frac{1}{2}ac\sin B=\frac{1}{2}\left(60\right)\left(50\right)(\frac{4}{5}\times \frac{7}{25}+\frac{3}{5}\times \frac{24}{25})=1200$