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 angle at X

Sum of angles in triangle: 180° - 51° - 76° = 53° (angle X)

Step2: Apply Law of Sines

Side opposite 51° (angle Y) is 2.6; side opposite 76° (angle Z) is z. So $\frac{\sin(51^\circ)}{2.6} = \frac{\sin(76^\circ)}{z}$

Step3: Solve for z

$z = \frac{2.6 \cdot \sin(76^\circ)}{\sin(51^\circ)}$

Step4: Calculate values

$\sin(76^\circ) \approx 0.9703$, $\sin(51^\circ) \approx 0.7771$; $z \approx \frac{2.6 \cdot 0.9703}{0.7771} \approx 3.2$

Answer:

B. 3.2 units