Respuesta :
Answer:
Therefore A = [tex]cos^{-1}[/tex](0.4338) = 64.29°
Step-by-step explanation:
i) Law of cosines: [tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] – 2bccos(A)
ii) XZ = a = 16 , YZ = b = 12, XY = 17, ∠Y = ∠A
iii) [tex]16^{2}[/tex] = [tex]12^{2}[/tex] + [tex]17^{2}[/tex] - (2[tex]\times[/tex] 12[tex]\times[/tex] 17[tex]\times[/tex] cos(A))
⇒ 256 = 144 + 289 - 408cos(A)
⇒ 256 - 144 - 289 = -408cos(A)
⇒ -177 = -408cos(A)
⇒ cos A = [tex]\frac{-177}{-408}[/tex] = 0.4338
Therefore A = [tex]cos^{-1}[/tex](0.4338) = 64.29°
