Question

If $\cos A=\frac{P}{a}$, $\cos B=\frac{9}{b}$, then find $\sin A$ and $\sin B$.

Answer 1

$\cos A=\frac{P}{a}=\frac{Base}{Hypotenuse}$

Hypotenuse $=P$, Base $=a$

By u\sin g Pythagoras theorem-

$Hypotenus{e}^2=Bas{e}^2+Perpendicula{r}^2$

$P^2=a^2+Perpendicula{r}^2$

$Perpendicular=\sqrt{(P^2-a^2)}$

$\sin A=\frac{Perpendicular}{Hypotenuse}$

$\sin A=\frac{\sqrt{(P^2-a^2)}}{P}$,

Similarly,

$\sin B=\frac{\sqrt{(9^2-b^2)}}{9}$,

$\sin B=\frac{\sqrt{(81-b^2)}}{9}$.

Hence, the this is solution.