In a triangle $\mathrm{ABC}, a=8, b=10$ and $c=12$. What is angle C equal to?

• A

  $\mathrm{A} / 2$
• B

  2 A
• C

  3A
• Correct answer
  D

  $3 \mathrm{~A} / 2$

Solution

$\frac{a}{\sin \mathrm{~A}}=\frac{b}{\sin \mathrm{~B}}=\frac{c}{\sin \mathrm{C}}$ $\frac{8}{\sin A}=\frac{12}{\sin C}$ $\Rightarrow \quad 8 \mathrm{C}=12 \mathrm{~A}$ $\mathrm{C}=\frac{12 \mathrm{~A}}{8}=\frac{3 \mathrm{~A}}{2}$.

Hence, the correct answer is option: 'D'.