Ъгли в триъгълник

[Гост]

[tex]\triangle ABC,\angle B-\angle A=90^\circ,AC=3BC,\angle A=?[/tex]

[Davids]

Синусова теорема:
$\frac{BC}{sin\angle A} = \frac{AC}{sin\angle B} = \frac{3BC}{sin(90° + \angle A)} = \frac{3BC}{cos\angle A}$
$\Rightarrow \frac{1}{sin\angle A} = \frac{3}{cos\angle A}$
$\Rightarrow cotg\angle A = 3$
$\angle A = arccotg(3) \approx 18.43°$