[tex3]\mathsf{
tg(45- \frac{x}{2}) = \frac{R}{\ell - R} = \frac{1 - tg(\frac x2)}{1 + tg(\frac x2)}\\
tg(\frac{x}{2})=y\\
(1−y)(ℓ−R)=R(1+y)(1−y)(ℓ−R)=R(1+y)\\
ℓ(ℓ−R)=R(ℓ+2R)ℓ(ℓ−R)=R(ℓ+2R)\\
\ell(\ell - R) = R(\ell +2R)\\
ℓ^2−Rℓ=Rℓ+2R^2\\
ℓ^2−2Rℓ=2R^2\\
(ℓ−R)^2=3R^2\\
ℓ=R(1±\sqrt3)\\
ℓ=R(1+\sqrt3))\\
y=\frac{1}{2+\sqrt3}=2−\sqrt3\\
tg(x) = \frac{2y}{1-y^2} = \frac{4-2\sqrt3}{1-7+4\sqrt3}=\frac{2-\sqrt3}{2\sqrt3-3} = \frac{1}{\sqrt3}=
30^o
}[/tex3]
(Solução:sousóeu -
viewtopic.php?f=4&t=59608&p=157672&hili ... +x#p157672)