Question

the law of cosines is used to find the measure of ∠z. to the nearest whole degree, what is the measure of ∠z? 16² = 18² + 19² - 2(18)(19)cos(z) 256 = 324 + 361 - (684)cos(z) 256 = 685 - (684)cos(z)

Explanation:

Step1: Rearrange the cosine - law equation

Starting with $256 = 685-684\cos(Z)$, we first isolate the term with $\cos(Z)$.
$684\cos(Z)=685 - 256$.

Step2: Calculate the right - hand side

$685−256 = 429$, so $684\cos(Z)=429$.
Then $\cos(Z)=\frac{429}{684}\approx0.6272$.

Step3: Find the angle

$Z=\cos^{-1}(0.6272)$. Using a calculator, $Z\approx51^{\circ}$.

Answer:

$51^{\circ}$