Question

which of the following equations could be used to find the value of x? the figure is not drawn to scale answer $\frac{x}{sin(46)}=\frac{30}{sin(32)}$ $\frac{sin(x)}{46}=\frac{sin(30)}{32}$ $cos x=\frac{104^{2}+30^{2}-46^{2}}{2(104)(30)}$ $\frac{x}{sin(46)}=\frac{32}{sin(30)}$

Explanation:

Step1: Recall the Law of Sines

The Law of Sines states that in a triangle $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$, where $a,b,c$ are the side - lengths of the triangle and $A,B,C$ are the opposite angles respectively.

Step2: Identify the sides and angles in the given triangle

We are given a triangle with side - length $x$ opposite an angle of $46^{\circ}$, side - length $32$ opposite an angle of $30^{\circ}$.

Step3: Apply the Law of Sines

According to the Law of Sines, we have $\frac{x}{\sin(46)}=\frac{32}{\sin(30)}$.

Answer:

$\frac{x}{\sin(46)}=\frac{32}{\sin(30)}$ (the fourth option)