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)

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \( a^{2}=b^{2}+c^{2}-2bc\cos(A)\), where \(a\) is the side opposite angle \(A\), and \(b\) and \(c\) are the other two sides.

Step2: Identify the sides and angle in the triangle

In \(\triangle XYZ\), let \(a = x\), \(b = 5\), \(c = 8\), and \(A=55^{\circ}\).

Step3: Substitute into the Law of Cosines formula

Substituting the values into the formula \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\), we get \(x^{2}=5^{2}+8^{2}-2(5)(8)\cos(55^{\circ})\).

Answer:

\(x^{2}=5^{2}+8^{2}-2(5)(8)\cos(55^{\circ})\) (the second option)