Question

find the length of side c.
b = 26
a = 19
c = ?
law of cosines: $c^2 = a^2 + b^2 - 2ab \cdot \cos(c)$
round your answer to the nearest hundredth

Explanation:

Step1: Identify known values

We know \(a = 19\), \(b = 26\), and \(\angle C = 31^\circ\). We use the Law of Cosines formula \(c^{2}=a^{2}+b^{2}-2ab\cdot\cos(C)\).

Step2: Substitute values into formula

Substitute \(a = 19\), \(b = 26\), and \(\cos(31^\circ)\approx0.8572\) into the formula:

$$
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Step3: Solve for \(c\)

Take the square root of \(c^{2}\) to find \(c\):
\(c=\sqrt{189.9864}\approx13.78\)

Answer:

\(13.78\)