Question

which equation is correct and can be used to solve for the value of z? law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ $\frac{sin(51^{circ})}{2.6}=\frac{sin(76^{circ})}{z}$ $\frac{sin(51^{circ})}{2.6}=\frac{sin(53^{circ})}{z}$ $\frac{sin(76^{circ})}{2.6}=\frac{sin(51^{circ})}{z}$ $\frac{sin(76^{circ})}{2.6}=\frac{sin(53^{circ})}{z}$

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 of the triangle and $a$, $b$, $c$ are the lengths of the sides opposite to those angles respectively.

Step2: Identify the angles and sides

In the given triangle, we have an angle of $76^{\circ}$ opposite a side of length $2.6$ and an angle of $51^{\circ}$ opposite a side of length $z$.

Step3: Apply the law of sines

According to the law of sines, we get $\frac{\sin(76^{\circ})}{2.6}=\frac{\sin(51^{\circ})}{z}$.

Answer:

$\frac{\sin(76^{\circ})}{2.6}=\frac{\sin(51^{\circ})}{z}$ (the third - option)