Question

find the length of side c.
law of cosines ( c^{2}=a^{2}+b^{2}-2abcdotcos (c) )

Explanation:

Step1: Identify given values

We know \(a = 13\), \(b = 18\), and \(\angle C=43^\circ\). The Law of Cosines formula for side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos(C)\).

Step2: Substitute values into formula

Substitute \(a = 13\), \(b = 18\), and \(\cos(43^\circ)\) (we can calculate \(\cos(43^\circ)\approx0.7314\)) into the formula:

$$
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Step3: Take square root

Take the square root of \(c^{2}\) to find \(c\):

$$ c=\sqrt{150.6048}\approx12.27 $$

Answer:

The length of side \(c\) is approximately \(12.27\).