Question

which is the best approximation of the value of x? use the law of sines to find the answer. 1.5 units 2.1 units 2.9 units 3.6 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 $180^{\circ}$. 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 $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$. We know one side $y = 2$ and its opposite angle $\angle Y=75^{\circ}$, and we want to find side $x$ opposite $\angle X = 55^{\circ}$. So, $\frac{\sin X}{x}=\frac{\sin Y}{y}$, which gives $x=\frac{y\sin X}{\sin Y}$.

Step3: Substitute the values

Substitute $y = 2$, $\angle X = 55^{\circ}$, and $\angle Y=75^{\circ}$ into the formula. $\sin55^{\circ}\approx0.819$, $\sin75^{\circ}\approx0.966$. Then $x=\frac{2\times0.819}{0.966}\approx1.7$. The closest value to $1.7$ among the options is $1.5$ units.

Answer:

1.5 units