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The shape ABC is an triangle, AB = 64 mi, BC = 32.6 mi. Angle ABC is 74 degrees. Using the cosine rule, calculate the distance of AC

Jan 20, 2020

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The shape ABC is an triangle, AB = 64 mi, BC = 32.6 mi. Angle ABC is 74 degrees.

Using the cosine rule, calculate the distance of AC

$$\begin{array}{|rcll|} \hline AC^2 &=& AB^2+BC^2-2*AB*BC*\cos(74^\circ) \\ AC^2 &=& 64^2+32.6^2-2*64*32.6*\cos(74^\circ) \\ AC^2 &=& 4096+1062.76-4172.8*\cos(74^\circ) \\ AC^2 &=& 4096+1062.76-4172.8*0.27563735582 \\ AC^2 &=& 5158.76-1150.17955835 \\ AC^2 &=& 4008.58044165 \\ \mathbf{AC} &=& \mathbf{63.3133512116} \\ \hline \end{array}$$

AC is 63.3 mi

Jan 20, 2020