Question

Sa se afle ariile următoarelor triunghiuri:
a) triunghiul ABC isoscel, AB=AC=12 cm și B=30 grade

b) triunghiul ABC,C=90 grade, A=30 grade, AB=16 cm

c) triunghiul ABC,A=90 grade,B=45 grade, BC=16 cm

VA ROG AM NEVOIE URGENT!

Answer 1

Explicație pas cu pas:

a)

$A = \frac{AB \times AC \times sin(B)}{2} = \frac{12 \times 12 \times \sin(30) }{2} = 72 \times \frac{1}{2} = 36 \: {cm}^{2}$

b) ∢B = 30° => BC = AB ÷ 2 = 16 ÷ 2 = 8 cm

AC² = AB² - BC² = 16² - 8² = 192

$AC = 8 \sqrt{3} \: cm$

$A = \frac{AC \times BC}{2} = \frac{8 \sqrt{3} \times 8 }{2} = 32 \sqrt{3} \: {cm}^{2}$

sau:

$A = \frac{AC \times AB \times sin(A)}{2} = \frac{8 \sqrt{3} \times 16 \times \sin(30) }{2} = 64 \sqrt{3} \times \frac{1}{2} = 32 \sqrt{3}\: {cm}^{2}$

c) ∢B = 45°

$= > AB = AC = \frac{BC}{\sqrt{2}} = \frac{16}{ \sqrt{2}} = 8 \sqrt{2} \: cm$

$A = \frac{AB \times AC}{2} = \frac{8 \sqrt{2} \times 8 \sqrt{2} }{2} = 64 \: {cm}^{2}$

sau:

$A = \frac{AB \times BC \times sin(B)}{2} = \frac{8 \sqrt{2} \times 16 \times \sin(45) }{2} = 64 \sqrt{2} \times \frac{ \sqrt{2} }{2} = 64 \: {cm}^{2}$