Giải câu 2 trang 75 toán VNEN 9 tập 1.
a) $\widehat{B}$ = $90^{\circ}$ - $\widehat{C}$ = $90^{\circ}$ - $30^{\circ}$ = $60^{\circ}$
sinB = $\frac{CA}{CB}$ $\Rightarrow $ CB = $\frac{CA}{sinB}$ = $\frac{8}{sin60}$ = $\frac{16}{\sqrt{3}}$ (cm)
AB = CB.sinC = $\frac{16}{\sqrt{3}}$.sin30 = $\frac{8}{\sqrt{3}}$ (cm)
b) $\widehat{B}$ = $90^{\circ}$ - $\widehat{C}$ = $90^{\circ}$ - $45^{\circ}$ = $45^{\circ}$
=> Tam giác ABC vuông cân tại A $\Rightarrow $ AC = AB = 12 cm
sinC = $\frac{AB}{CB}$ $\Rightarrow $ CB = $\frac{CA}{sinB}$ = $\frac{12}{sin45}$ = 12$\sqrt{2}$ (cm)
c) $\widehat{C}$ = $90^{\circ}$ - $\widehat{B}$ = $90^{\circ}$ - $35^{\circ}$ = $55^{\circ}$
sinB = $\frac{AC}{CB}$ $\Rightarrow $ AC = CB.sinB = 10.sin35 = 5,74 cm
AB = CB.sinC = 10.sin55 = 8,19 cm
d) BC = $\sqrt{AB^{2} + AC^{2}}$ = $\sqrt{10^{2} + 24^{2}}$ = 26 cm
sin B = $\frac{AC}{CB}$ = $\frac{24}{26}$ = $\frac{12}{13}$
$\Rightarrow $ $\widehat{B}$ = $67,38^{\circ}$
$\widehat{B}$ = $90^{\circ}$ - $\widehat{C}$ = $90^{\circ}$ - $67,38^{\circ}$ = $22,62^{\circ}$.