PUCCAMP 2026 – Lei dos Cossenos | Questão 28 Resolvida

Observe o trapézio ABCD, com alguns dados fornecidos na figura:

Aplicando a lei dos cossenos no triângulo BEC , a medida de $\overline{BC}$ , em centímetros, será

(A) $\dfrac{\sqrt{25+32 \cos^2 40^{\circ}-40\sqrt{2}\cdot \cos 40^{\circ} \cdot \text{sen} 85^{\circ} }}{\cos 40^{\circ}}$

(B) $\dfrac{\sqrt{25+32\cos^2 40^{\circ}-40\sqrt{2}\cdot \text{sen} 40^{\circ} \cdot \cos 85^{\circ} }}{\text{sen} 40^{\circ}}$

(C) $\dfrac{\sqrt{25+32 \text{sen}^2 40^{\circ}-40\sqrt{2}\cdot \text{sen} 40^{\circ} \cdot \cos 85^{\circ} }}{\text{sen} 40^{\circ}}$

(D) $\dfrac{\sqrt{25+32\cos^2 40^{\circ}-40\sqrt{2}\cdot \cos 40^{\circ} \cdot \cos 85^{\circ} }}{\cos 40^{\circ}}$

(E) $\dfrac{\sqrt{25+32\cos^2 40^{\circ}-40\sqrt{2}\cdot \text{sen} 40^{\circ} \cdot \cos 85^{\circ} }}{\cos 40^{\circ}}$

Matemática para Vestibulares