Question

find the measure of angle c.
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Rearranging for \(\cos C\), we get \(\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).
Substitute \(a = 11\), \(b = 12\), and \(c = 20\) into the formula:
\(\cos C=\frac{11^{2}+12^{2}-20^{2}}{2\times11\times12}\)

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Step2: Find the angle \(C\)

Since \(C=\cos^{-1}(\cos C)\), then \(C=\cos^{-1}(-0.511)\)
Using a calculator, \(C\approx120.7^{\circ}\)

Answer:

\(120.7\)