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

Sum of angles in triangle: 180° - 75° - 50° = 55°

Step2: Apply Law of Sines

Side opposite 50° (Z) is 2; side opposite 55° (X) is x. So $\frac{\sin(55^\circ)}{x} = \frac{\sin(50^\circ)}{2}$

Step3: Solve for x

$x = \frac{2 \cdot \sin(55^\circ)}{\sin(50^\circ)}$

Step4: Calculate approximate value

$\sin(55^\circ) \approx 0.8192$, $\sin(50^\circ) \approx 0.7660$. $x \approx \frac{2 \cdot 0.8192}{0.7660} \approx 2.1$

Answer:

B. 2.1 units