Giải câu 1 trang 77 toán VNEN 9 tập 1

Giải câu a) b = 5cm, c = 12cm 

a = $\sqrt{b^{2} + c^{2}}$ = $\sqrt{5^{2} + 12^{2}}$ = 13cm

sin B = $\frac{b}{a}$ = $\frac{5}{13}$ $\Rightarrow $ $\widehat{B}$ = $22,6^{\circ}$ ; $\widehat{C}$ = $90^{\circ}$ - $22,6^{\circ}$ = $67,4^{\circ}$

Giải câu b) a = 8cm, b = 6cm 

c = $\sqrt{a^{2} - b^{2}}$ = $\sqrt{8^{2} - 6^{2}}$ = 2$\sqrt{7}$cm

sinB = $\frac{b}{a}$ = $\frac{6}{8}$ $\Rightarrow $ $\widehat{B}$ = $48,6^{\circ}$ ; $\widehat{C}$ = $90^{\circ}$ - $48,6^{\circ}$ = $41,4^{\circ}$

Giải câu c) b = 6cm, $\widehat{B}$ = $60^{\circ}$

$\widehat{C}$ = $90^{\circ}$ - $\widehat{B}$ = $90^{\circ}$ - $60^{\circ}$ = $30^{\circ}$

sinB = $\frac{b}{a}$ = $\frac{6}{a}$ $\Rightarrow $ a = 4$\sqrt{3}$ cm, c = $\sqrt{a^{2} - b^{2}}$ = $\sqrt{(4\sqrt{3})^{2} - 6^{2}}$ = 2$\sqrt{3}$ cm

Giải câu d) a = 10cm, $\widehat{C}$ = $25^{\circ}$

$\widehat{B}$ = $90^{\circ}$ - $\widehat{C}$ = $90^{\circ}$ - $25^{\circ}$ = $65^{\circ}$

sinB = $\frac{b}{a}$ = $\frac{b}{10}$ $\Rightarrow $ b = 9,06 cm, c = $\sqrt{a^{2} - b^{2}}$ = $\sqrt{10^{2} - 9,06^{2}}$ = 4,23 cm.