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

Explanation:

Step1: Identify the sides for cosine - law

In $\triangle{WUV}$, let $w = 15$, $u = 6$, $v = 12$. We want to find $\angle{U}$, and the cosine - law formula is $w^{2}=u^{2}+v^{2}-2uv\cos U$.

Step2: Rearrange the cosine - law formula

We can rewrite the formula for $\cos U$ as $\cos U=\frac{u^{2}+v^{2}-w^{2}}{2uv}$. Substitute $u = 6$, $v = 12$, and $w = 15$ into the formula: [ \begin{align*} \cos U&=\frac{6^{2}+12^{2}-15^{2}}{2\times6\times12}\ &=\frac{36 + 144-225}{144}\ &=\frac{180 - 225}{144}\ &=\frac{-45}{144}\ &=-\frac{5}{16} \end{align*} ]

Step3: Find the angle

Then $U=\cos^{-1}(-\frac{5}{16})$. Using a calculator, $U\approx108.2^{\circ}$

Answer:

$108.2$