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: Find the third - angle

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

Step2: Apply the law of sines

According to the law of sines $\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}$. Here, if we consider $\frac{\sin(50^{\circ})}{y}=\frac{\sin(75^{\circ})}{2}$.
Then, $y=\frac{2\times\sin(50^{\circ})}{\sin(75^{\circ})}$.
We know that $\sin(50^{\circ})\approx0.766$ and $\sin(75^{\circ})=\sin(45^{\circ} + 30^{\circ})=\sin45^{\circ}\cos30^{\circ}+\cos45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.966$.
So, $y=\frac{2\times0.766}{0.966}\approx1.6$.

Answer:

1.6 units