Question

the law of cosines is used to find the measure of $angle z$. to the nearest whole degree, what is the measure of $angle z$?$\bigcirc$ $41^circLXB0\bigcirc$ $51^circ$$\bigcirc$ $57^circ$$16^{2}=18^{2}+19^{2}-2(18)(19)cos(z)$$256=324+361-(684)cos(z)$$256=685-(684)cos(z)$$-429=-(684)cos(z)$

Explanation:

Step1: Isolate $\cos(Z)$

$\cos(Z) = \frac{-429}{-684}$

Step2: Simplify the fraction

$\cos(Z) = \frac{429}{684} \approx 0.6272$

Step3: Calculate $\angle Z$

$\angle Z = \arccos(0.6272)$

Answer:

$51^\circ$ (Option C)