Question

In a right angled $\Delta ABC,\angle B={90}^{\circ }$ and $\cos A=\frac{15}{17}$, then $\sin c$ equals to

• A. $\frac{8}{17}$
• B. $\frac{8}{15}$
• C. $\frac{17}{15}$
• D. $\frac{15}{17}$

Answer 1

The correct option is D $\frac{15}{17}$

Since, $\cos A=\frac{15}{17}$
$\Rightarrow$ Base $\left(AB\right)=15$ and hypotenuse $\left(AC\right)=17$
$\therefore$ perpendicular $\left(BC\right)=\sqrt{(17{)}^2-(15{)}^2}=\sqrt{64}=8$
To find $\sin C$, perpendicular is $AB$, base is $BC$.
$\therefore \sin C=\frac{AB}{AC}=\frac{15}{17}$
Hence, option D is correct.