find m∠z. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠z = °

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for finding an angle in a triangle is $\cos Z=\frac{x^{2}+y^{2}-z^{2}}{2xy}$, where $x = 5$, $y=9$, and $z = 11$. So, $\cos Z=\frac{5^{2}+9^{2}-11^{2}}{2\times5\times9}$.

Step2: Calculate the numerator and denominator

First, calculate the numerator: $5^{2}+9^{2}-11^{2}=25 + 81-121= -15$. The denominator is $2\times5\times9 = 90$. So, $\cos Z=\frac{-15}{90}=-\frac{1}{6}$.

Step3: Find the angle

$Z=\cos^{-1}(-\frac{1}{6})$. Using a calculator, $Z\approx 99.6^{\circ}$.

Answer:

$99.6$