Question

what is the value of z, rounded to the nearest tenth? use the law of sines to find the answer. 2.7 units 3.2 units 4.5 units 5.3 units law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third - angle be $\angle X$. So, $\angle X=180^{\circ}-(51^{\circ}+76^{\circ}) = 53^{\circ}$.

Step2: Apply the law of sines

According to the law of sines, $\frac{\sin(Z)}{z}=\frac{\sin(X)}{x}$. We know that $x = 2.6$, $\angle X = 53^{\circ}$, and $\angle Z=76^{\circ}$. So, $\frac{\sin(76^{\circ})}{z}=\frac{\sin(53^{\circ})}{2.6}$.

Step3: Solve for z

Cross - multiply to get $z\times\sin(53^{\circ})=2.6\times\sin(76^{\circ})$. Then $z=\frac{2.6\times\sin(76^{\circ})}{\sin(53^{\circ})}$. Since $\sin(76^{\circ})\approx0.9703$ and $\sin(53^{\circ})\approx0.7986$, $z=\frac{2.6\times0.9703}{0.7986}=\frac{2.52278}{0.7986}\approx3.2$.

Answer:

3.2 units