Question

find the length of side x. round to the nearest tenth.

x=

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Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\), where \(a = 18.2\), \(b=14\), and \(C = 72^{\circ}\).
Substitute the values: \(x^{2}=18.2^{2}+14^{2}-2\times18.2\times14\times\cos(72^{\circ})\)
First, calculate \(18.2^{2}=331.24\), \(14^{2} = 196\), and \(\cos(72^{\circ})\approx0.3090\)
Then \(2\times18.2\times14\times0.3090=2\times18.2\times14\times0.3090 = 156.9144\)
So \(x^{2}=331.24 + 196-156.9144\)

Step2: Simplify the right - hand side

\(x^{2}=331.24+196 - 156.9144=370.3256\)

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{370.3256}\approx19.2\)

Answer:

\(19.2\)