Question

quiz 8: solve right, scalene, and obtuse tria
6 points possible answered: 3/6
question 4
find the length of side x. round to the nearest tenth.
triangle with sides 10.4, 8, angle 72° between them, and side x opposite?
x =
question help: video ebook

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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 \(a = 10.4\), \(b = 8\), and \(C=72^{\circ}\).
Substitute the values into the formula:
\(x^{2}=10.4^{2}+8^{2}-2\times10.4\times8\times\cos(72^{\circ})\)
First, calculate \(10.4^{2}=108.16\), \(8^{2} = 64\), and \(\cos(72^{\circ})\approx0.3090\).
Then \(2\times10.4\times8\times0.3090=2\times10.4\times8\times0.3090 = 51.9264\).
So \(x^{2}=108.16 + 64-51.9264\).

Step2: Simplify the right - hand side

\(x^{2}=108.16+64 - 51.9264=120.2336\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{120.2336}\approx10.965\).
Round to the nearest tenth: \(x\approx11.0\).

Answer:

\(11.0\)