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Question

Use the Law of Cosines to solve the triangle. $C=108^{\circ}, \quad a=10, \quad b=7$

Solution

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Step 1
1 of 4

Begin by determining side $c$. By using the standard form of the Law of Cosines

\begin{aligned} c^2&=a^2+b^2-2ab\cos C\\[10pt] &=(10)^2+(7)^2-2(10)(7)\cos 108^{\circ}\\[10pt] &\approx192.26 \end{aligned}

from which

$\boxed{c\approx13.87}$

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