Question

in order to make a precise cut from point q to point s using a saw, alfonso needs to know the angle measure for the angle whose vertex is s. based on the diagram below, which equation could alfonso use to determine the measure of angle s? not drawn to scale $9^{2}=10^{2}+11^{2}-2(10)(11)\cos s$ $10^{2}=9^{2}+11^{2}-2(9)(11)\cos s$ $9^{2}=10^{2}+11^{2}+2(10)(11)\cos s$ $10^{2}=9^{2}+11^{2}+2(9)(11)\cos s$

Explanation:

Step1: Recall the Law of Cosines

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

Step2: Identify the sides and the angle in the triangle

In \(\triangle QRS\), if we want to find \(\cos S\), the side opposite angle \(S\) is \(QR = 10\) in, \(QS=9\) in, and \(RS = 11\) in.
Substitute into the Law of Cosines formula: \(10^{2}=9^{2}+11^{2}-2(9)(11)\cos S\)

Answer:

\(10^{2}=9^{2}+11^{2}-2(9)(11)\cos S\)