Question

Dado a seguinte equação:
$Sen \alpha = \frac{R}{R+h}$
Demonstre como:
$R= \frac{h.sen \alpha }{1-sen \alpha }$

Answer 1

$\sin\alpha=\frac{R}{R+h}$

$\sin\alpha(R+h)=R$

$R\sin\alpha+h\sin\alpha=R$

$R\sin\alpha-R+h\sin\alpha=0$

$R(\sin\alpha-1)+h\sin\alpha=0$

$R(\sin\alpha-1)=-h\sin\alpha$

$R=-\frac{h\sin\alpha}{\sin\alpha-1}$

$R=\frac{h\sin\alpha}{1-\sin\alpha}$