Question

Sa se calculeze sin A,stiind ca in triunghiul ABC se cunosc AB=4 BC=2 si m(<C)=60​

Answer 1

Explicație pas cu pas:

Din T.S⇒BC/sinA=AB/sinC⇒2/sinA=4/√3/2⇒2/sinA=8√3/3⇒

⇒sinA=2/(8√3/3)⇒sinA=√3/4

Bafta!

Answer 2

AB = 4  ⇔  c = 4

BC = 2  ⇔  a = 2

m(∢C) = 60°

Teorema sinusurilor:

$\dfrac{c}{\sin(\sphericalangle C)} = \dfrac{a}{\sin(\sphericalangle A)} \\ \\ \Rightarrow \dfrac{4}{\sin(60^\circ)} = \dfrac{2}{\sin(\sphericalangle A)} \\ \\ \Rightarrow \dfrac{4\cdot 2}{\sqrt 3} = \dfrac{2}{\sin(\sphericalangle A)} \\ \\\\\Rightarrow \sin(\sphericalangle A) = \dfrac{\sqrt 3}{4}$