Question

question 3
find the length of side x. round to the nearest tenth.

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Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 7.8\), \(b = 6\), and \(C=72^{\circ}\).
So, \(x^{2}=7.8^{2}+6^{2}-2\times7.8\times6\times\cos(72^{\circ})\).
First, calculate \(7.8^{2}=60.84\), \(6^{2} = 36\), and \(\cos(72^{\circ})\approx0.3090\).
Then \(2\times7.8\times6\times0.3090=2\times46.8\times0.3090 = 93.6\times0.3090\approx28.9224\).
Now, \(x^{2}=60.84 + 36-28.9224\).

Step2: Simplify the expression

\(x^{2}=60.84+36 - 28.9224=96.84-28.9224 = 67.9176\).

Step3: Find \(x\)

Take the square root of \(x^{2}\), \(x=\sqrt{67.9176}\approx8.2\).

Answer:

\(8.2\)