Question

use the law of sines to find the value of y. round to the nearest tenth. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ 1.4 units 1.6 units 2.5 units 2.6 units

Explanation:

Step1: Identify angles and sides

Angle at Y: 75°, opposite side XZ=2; angle at Z: 50°, opposite side XY=y.

Step2: Apply Law of Sines

$\frac{\sin(75^\circ)}{2} = \frac{\sin(50^\circ)}{y}$

Step3: Solve for y

$y = \frac{2 \cdot \sin(50^\circ)}{\sin(75^\circ)}$

Step4: Calculate value

$\sin(50^\circ) \approx 0.7660$, $\sin(75^\circ) \approx 0.9659$, $y \approx \frac{2 \cdot 0.7660}{0.9659} \approx 1.6$

Answer:

B. 1.6 units