Question

Calcule o valor da incógnita representada no triângulo ABC (Anexo)

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Answer 1

Resposta:

$\boxed{\mathtt{\alpha \approx 83,6^o}}$

Explicação passo-a-passo:

Pela Lei dos Cossenos,

$\\ \displaystyle \mathsf{4^2 = 3^2 + 3^2 - 2 \cdot 3 \cdot 3 \cdot \cos \alpha} \\\\ \mathsf{16 = 9 + 9 - 18 \cdot \cos \alpha} \\\\ \mathsf{16 = 18 - 18 \cdot \cos \alpha} \\\\ \mathsf{- 2 = - 18 \cdot \cos \alpha} \\\\ \mathsf{\cos \alpha = \frac{1}{9}} \\\\ \boxed{\boxed{\mathsf{\alpha = cos^{- 1} \frac{1}{9}}}}$