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 angle at X

First, calculate $\angle X$ using the triangle angle sum (180°):
$\angle X = 180^\circ - 75^\circ - 50^\circ = 55^\circ$

Step2: Apply Law of Sines

Match sides to opposite angles. Side $x$ is opposite $\angle X=55^\circ$, side 2 is opposite $\angle Z=50^\circ$:
$\frac{x}{\sin(55^\circ)} = \frac{2}{\sin(50^\circ)}$

Step3: Solve for x

Rearrange to isolate $x$ and compute the value:
$x = \frac{2 \times \sin(55^\circ)}{\sin(50^\circ)}$
Using $\sin(55^\circ) \approx 0.8192$, $\sin(50^\circ) \approx 0.7660$:
$x \approx \frac{2 \times 0.8192}{0.7660} \approx 2.1$

Answer:

2.1 units