Explicație pas cu pas:
a)
[tex]A = \frac{AB \times AC \times sin(B)}{2} = \frac{12 \times 12 \times \sin(30) }{2} = 72 \times \frac{1}{2} = 36 \: {cm}^{2} [/tex]
b) ∢B = 30° => BC = AB ÷ 2 = 16 ÷ 2 = 8 cm
AC² = AB² - BC² = 16² - 8² = 192
[tex]AC = 8 \sqrt{3} \: cm [/tex]
[tex]A = \frac{AC \times BC}{2} = \frac{8 \sqrt{3} \times 8 }{2} = 32 \sqrt{3} \: {cm}^{2} [/tex]
sau:
[tex]A = \frac{AC \times AB \times sin(A)}{2} = \frac{8 \sqrt{3} \times 16 \times \sin(30) }{2} = 64 \sqrt{3} \times \frac{1}{2} = 32 \sqrt{3}\: {cm}^{2} [/tex]
c) ∢B = 45°
[tex] = > AB = AC = \frac{BC}{\sqrt{2}} = \frac{16}{ \sqrt{2}} = 8 \sqrt{2} \: cm [/tex]
[tex]A = \frac{AB \times AC}{2} = \frac{8 \sqrt{2} \times 8 \sqrt{2} }{2} = 64 \: {cm}^{2} [/tex]
sau:
[tex]A = \frac{AB \times BC \times sin(B)}{2} = \frac{8 \sqrt{2} \times 16 \times \sin(45) }{2} = 64 \sqrt{2} \times \frac{ \sqrt{2} }{2} = 64 \: {cm}^{2} [/tex]
