Question

which of the following equations could be used to find the value of x? the figure is not drawn to scale answer $\frac{x}{sin(80)}=\frac{40}{sin(22)}$ $x = \frac{1}{2}(40)(22)sin(80)$ $x^{2}=40^{2}+22^{2}-2(40)(22)cos(80)$ $x^{2}=40^{2}+80^{2}-2(40)(80)cos(22)$

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\) is \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). In the given triangle, if \(a = 40\), \(b = 22\) and the included - angle \(\theta=80^{\circ}\) and the side opposite to the \(80^{\circ}\) angle is \(x\).

Step2: Apply the Law of Cosines

Substitute \(a = 40\), \(b = 22\) and \(\theta = 80^{\circ}\) into the Law - of - Cosines formula. We get \(x^{2}=40^{2}+22^{2}-2(40)(22)\cos(80^{\circ})\).

Answer:

\(x^{2}=40^{2}+22^{2}-2(40)(22)\cos(80^{\circ})\)