Cho \(\Delta ABC\) có \(\widehat A = 135^\circ ,\widehat C = 15^\circ \) và \(b = 12\). Khi đó:

a) \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = \frac{1}{2}R\).

b) \(a = 12\sqrt 2 \).

c) \(c \approx 8,21\).

d) \(R = 15\).

a) S, b) Đ, c) S, d) S

a) \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R\)

b) Ta có \(\widehat B = 180^\circ  - \left( {\widehat A + \widehat C} \right) = 180^\circ  - \left( {135^\circ  + 15^\circ } \right) = 30^\circ \).

Ta có \(\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R\)\( \Leftrightarrow \frac{a}{{\sin 135^\circ }} = \frac{b}{{\sin 30^\circ }} = \frac{c}{{\sin 15^\circ }} = 2R\).

Suy ra \(a = \frac{{12.\sin 135^\circ }}{{\sin 30^\circ }} = 12\sqrt 2 \).

c) Ta có \(c = \frac{{12.\sin 15^\circ }}{{\sin 30^\circ }} \approx 6,21\).

d) Ta có \(R = \frac{{12}}{{2\sin 30^\circ }} = 12\).