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

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for finding an angle in a triangle $\triangle UVW$ is $\cos U=\frac{VW^{2}+UW^{2}-UV^{2}}{2\cdot VW\cdot UW}$. Here, $UW = 5$, $VW=7$, and $UV = 9$. So, $\cos U=\frac{7^{2}+5^{2}-9^{2}}{2\times7\times5}$.

Step2: Calculate the numerator and denominator

First, calculate the numerator: $7^{2}+5^{2}-9^{2}=49 + 25-81=13$. The denominator is $2\times7\times5 = 70$. So, $\cos U=\frac{13}{70}$.

Step3: Find the angle

$U=\cos^{-1}(\frac{13}{70})$. Using a calculator, $U\approx79.3^{\circ}$.

Answer:

$79.3$