Question

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

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third angle be $A$. So $A=180^{\circ}-75^{\circ}-50^{\circ}=55^{\circ}$.

Step2: Apply the law of sines

We know that $\frac{\sin(50^{\circ})}{y}=\frac{\sin(75^{\circ})}{2}$. Cross - multiply to get $y\times\sin(75^{\circ}) = 2\times\sin(50^{\circ})$.

Step3: Solve for $y$

$y=\frac{2\times\sin(50^{\circ})}{\sin(75^{\circ})}$. Since $\sin(50^{\circ})\approx0.766$ and $\sin(75^{\circ})\approx0.966$, then $y=\frac{2\times0.766}{0.966}\approx1.6$.

Answer:

1.6 units