Question

Observe o triângulo abaixo e determine o valor do lado BC. Use: Cosseno 120º = MENOS o cosseno de 60º


24 cm

32√2 cm

17,43 cm

17,56 cm

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Lei~dos~cossenos}\\\sf a^2=b^2+c^2-2\cdot b\cdot c\cdot cos(\theta)\end{array}}$

$\large\boxed{\begin{array}{l}\sf BC^2= AB^2+AC^2-2\cdot AB\cdot AC\cdot cos(120^\circ)\\\sf BC^2=20^2+12^2-\backslash\!\!\!2\cdot20\cdot12\cdot\bigg(-\dfrac{1}{\backslash\!\!\!2}\bigg)\\\sf BC^2=400+144+240\\\sf BC^2=784\\\sf BC=\sqrt{784}\\\sf BC=28\\\boldsymbol{ corrija~o~gabarito} \end{array}}$