Question

eddie solved for the length of side c in \\( \triangle cbd \\) using the law of cosines formula, \\( c ^ { 2 } = a ^ { 2 } + b ^ { 2 } - 2 a b \cos c \\). sophia wants to solve for the side length of b. which equation could sophia use to solve for the side length of b, given the other two side lengths and the measure of their included angle?

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(x^{2}=y^{2}+z^{2}-2yz\cos X\), where \(x\) is the side opposite angle \(X\), and \(y\) and \(z\) are the other two sides.

Step2: Identify the sides and angle for solving \(b\)

In \(\triangle CBD\), if we want to solve for \(b\), the side opposite angle \(B\) is \(b\), and the other two sides are \(a\) and \(c\).

Step3: Apply the Law of Cosines formula for \(b\)

Substitute into the formula: \(b^{2}=a^{2}+c^{2}-2ac\cos B\)

Answer:

\(b^{2}=a^{2}+c^{2}-2ac\cos B\)