Question

The area of a triangle is $12sq.cm.$. Two sides are $6cm$ and $12cm$. The included angle is:

• A. ${\cos }^{-1}\left(\frac{1}{3}\right)$
• B. ${\cos }^{-1}\left(\frac{1}{6}\right)$
• C. ${\sin }^{-1}\left(\frac{1}{6}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Answer 1

Answer: (D)

${\sin }^{-1}\left(\frac{1}{3}\right)$

Area of $△ABC$ $=12{cm}^2$
$\frac{1}{2}\times BC\times AD=12$
$\frac{1}{2}\times 12\times AD=12$
$AD=2cm$
$\sin \theta =\frac{AD}{AB}=\frac{2}{6}=\frac{1}{3}$
$\theta ={\sin }^{-1}\left(\frac{1}{3}\right)$