Question

find the length of side c.
law of cosines: $c^{2}=a^{2}+b^{2}-2abcdot\cos c$
round your final answer to the nearest tenth.

Explanation:

Step1: Substitute values into formula

Given \(a = 13\), \(b = 18\), \(C=43^{\circ}\), substitute into \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
\(c^{2}=13^{2}+18^{2}-2\times13\times18\times\cos(43^{\circ})\)

Step2: Calculate each term

\(13^{2}=169\), \(18^{2}=324\), \(\cos(43^{\circ})\approx0.7314\), \(2\times13\times18 = 468\).
\(c^{2}=169 + 324-468\times0.7314\)
\(c^{2}=493-342.3952\)

Step3: Find \(c\)

\(c^{2}=150.6048\), \(c=\sqrt{150.6048}\approx12.3\)

Answer:

\(12.3\)