Question

find the value of x to the nearest tenth.
which of the following equations correctly sets up
the law of cosines to solve for x?
55² = 5² + 8² - 2(5)(8) cos(x)
√ x² = 5² + 8² - 2(5)(8) cos(55°)
x² = (5 + 8)² - 2(5)(8) cos(55°)
55² = 5² + 8² - 2(5)(8) cos(x)
complete
the value of x, rounded to the nearest tenth
is
done

Explanation:

Step1: Apply the Law of Cosines formula

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\), where \(a\), \(b\), \(c\) are sides of a triangle and \(A\) is the angle opposite to side \(a\). In this triangle, if \(a = x\), \(b = 5\), \(c = 8\), and \(A=55^{\circ}\), then the formula becomes \(x^{2}=5^{2}+8^{2}-2\times5\times8\times\cos(55^{\circ})\).

Step2: Calculate the value of \(x\)

First, calculate \(5^{2}=25\), \(8^{2}=64\), and \(2\times5\times8 = 80\). Then \(\cos(55^{\circ})\approx0.5736\).

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Answer:

\(6.6\)