what is the value of z, rounded to the nearest tenth? use the law of sines to find the answer.A) 2.7 unitsB) 3.2 unitsC) 4.5 unitsD) 5.3 units

We can change the law of sines a little bit to match our problem.

[tex]\sf\dfrac{sin(X)}{x}=\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}[/tex]

We know what angle Y is and what side y is, so let's use that along with angle Z and side z:

[tex]\sf\dfrac{sin(Y)}{y}=\dfrac{sin(Z)}{z}[/tex]

Plug in what we know:

[tex]\sf\dfrac{sin(51)}{2.6}=\dfrac{sin(76)}{z}[/tex]

Multiply 'z' to both sides:

[tex]\sf\dfrac{sin(51)}{2.6}z=sin(76)[/tex]

Divide sin(51)/2.6 to both sides:

[tex]\sf z=\dfrac{sin(76)(2.6)}{sin(51)}[/tex]

Plug it into your calculator.

[tex]\boxed{\sf z\approx 3.2}[/tex]