Question

find the measure of angle c.
a = 9
b = 3
c = 11
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 \(\cos C\) gives \(\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).
Substitute \(a = 9\), \(b = 3\), and \(c = 11\) into the formula:

$$
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Step2: Find the angle \(C\)

Use the inverse cosine function \(C=\cos^{-1}(\cos C)\).
\(C=\cos^{-1}(-0.574)\approx125.0^{\circ}\)

Answer:

\(125.0^{\circ}\)