Question

what is the value of z, rounded to the nearest tenth?
use the law of sines to find the answer.
○ 2.7 units
○ 3.2 units
○ 4.5 units
○ 5.3 units
law of sines: $\frac{sin(a)}{a} = \frac{sin(b)}{b} = \frac{sin(c)}{c}$

Explanation:

Step1: Find angle at X

The sum of angles in a triangle is $180^\circ$.
$\angle X = 180^\circ - 51^\circ - 76^\circ = 53^\circ$

Step2: Apply Law of Sines

Relate side $z$, side $XZ$, and their opposite angles.
$\frac{z}{\sin(76^\circ)} = \frac{2.6}{\sin(53^\circ)}$

Step3: Solve for z

Rearrange to isolate $z$ and calculate.
$z = \frac{2.6 \times \sin(76^\circ)}{\sin(53^\circ)}$
$\sin(76^\circ) \approx 0.9703$, $\sin(53^\circ) \approx 0.7986$
$z \approx \frac{2.6 \times 0.9703}{0.7986} \approx 3.2$

Answer:

3.2 units