Respuesta :

iGreen
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]

The value of z is 3.2 units.

What is the law of sines?

The law of sine or the sine law states that the proportion of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is additionally known as the sine rule.

For a triangle ABC the law of sine will be,

[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

In triangle XYZ given here,

The law of sine can be written as,

[tex]\frac{x}{sinX} =\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

here ∠Y and ∠Z is given so we write

[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

y=2.6

∠Y=51°

∠Z=76°

sin51°≈0.78

sin76°≈0.97

[tex]\frac{y}{sinY} =\frac{z}{sinZ}[/tex]

[tex]2.6/0.78=z/0.97[/tex]

[tex]z=3.2 units[/tex]

To learn more about the laws of sine please follow : brainly.com/question/16786029

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