Question

Considerando o triângulo da figura abaixo determine o valor do coseno b

Answer 1

Explicação passo-a-passo:

Pela lei dos cossenos:

$\sf 2^2=1^2+(\sqrt{6})^2-2\cdot1\cdot\sqrt{6}\cdot cos~\beta$

$\sf 4=1+6-2\sqrt{6}\cdot cos~\beta$

$\sf 4=7-2\sqrt{6}\cdot cos~\beta$

$\sf 2\sqrt{6}\cdot cos~\beta=7-4$

$\sf 2\sqrt{6}\cdot cos~\beta=3$

$\sf cos~\beta=\dfrac{3}{2\sqrt{6}}$

$\sf cos~\beta=\dfrac{3}{2\sqrt{6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}$

$\sf cos~\beta=\dfrac{3\sqrt{6}}{2\cdot6}$

$\sf cos~\beta=\dfrac{3\sqrt{6}}{12}$

$\sf \red{cos~\beta=\dfrac{\sqrt{6}}{4}}$