Question

If $\cos A=\frac{15}{17}$ then find $\sin A$.

Answer 1

$\cos A=\frac{15}{17}$

${\sin }^{2}A+{\cos }^{2}A=1$

${\sin }^2+{\left(\frac{15}{17}\right)}^2=1$

${\sin }^{2}A=1-{\left(\frac{15}{17}\right)}^2$

${\sin }^{2}A=1-\left(\frac{225}{289}\right)$

${\sin }^{2}A=\frac{289-225}{289}$

${\sin }^{2}A=\frac{64}{289}$

Taking square root on both sides

$\sin A=\frac{8}{17}$

Hence, $\sin A=\frac{8}{17}$