Question

two teams are pulling a heavy chest, located at point x. the teams are 4.8 meters away from each other. team a is 2.4 meters away from the chest, and team b is 3.2 meters away. their ropes are attached at an angle of 110°. which equation can be used to solve for angle a?
law of sines: \\( \frac{\sin(a)}{a}=\frac{\sin(b)}{b}=\frac{\sin(c)}{c} \\)

Explanation:

Step1: Recall the Law of Sines

The Law of Sines states that in a triangle, \(\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\), where \(A\), \(B\), \(C\) are angles and \(a\), \(b\), \(c\) are the lengths of the sides opposite to them respectively.

Step2: Identify the sides and angles

In the given triangle, angle \(X = 110^{\circ}\), side opposite to angle \(A\) is \(3.2\) (side \(XB\)), and the side opposite to angle \(X\) is \(4.8\).

Applying the Law of Sines: \(\frac{\sin(A)}{3.2}=\frac{\sin(110^{\circ})}{4.8}\)

Answer:

\(\frac{\sin(A)}{3.2}=\frac{\sin(110^{\circ})}{4.8}\) (the first option in the top - left box)