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 $ $\widehat{B}$ = $67,38^{\circ}$

$\widehat{B}$ = $90^{\circ}$ - $\widehat{C}$ = $90^{\circ}$ - $67,38^{\circ}$ = $22,62^{\circ}$.