Question

the law of cosines is used to find the measure of ∠z.
to the nearest whole degree, what is the measure of ∠z?
41°
47°
51°
57°
16² = 18² + 19² - 2(18)(19)cos(z)
256 = 324 + 361 - (684)cos(z)
256 = 685 - (684)cos(z)

Explanation:

Step1: Rearrange the formula

$$\begin{align*} 256&=685 - 684\cos(Z)\\ 684\cos(Z)&=685 - 256\\ 684\cos(Z)&=429 \end{align*}$$

Step2: Solve for \(\cos(Z)\)

$$ \cos(Z)=\frac{429}{684}\approx0.6272 $$

Step3: Find the angle \(Z\)

$$ Z=\cos^{-1}(0.6272)\approx51^{\circ} $$

Answer:

\(51^{\circ}\) (Option C)