find m∠s. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠s =
find m∠s. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠s =
Answer
Explanation:
Step1: Apply the Law of Cosines
The Law of Cosines formula for finding an angle in a triangle is $\cos(S)=\frac{QS^{2}+RS^{2}-QR^{2}}{2\cdot QS\cdot RS}$. Here, $QS = 11$, $RS=9$, and $QR = 12$. So, $\cos(S)=\frac{11^{2}+9^{2}-12^{2}}{2\times11\times9}=\frac{121 + 81-144}{198}=\frac{58}{198}\approx0.2929$.
Step2: Find the angle
We know that $S=\cos^{-1}(0.2929)$. Using a calculator, $S\approx72.9^{\circ}$.
Answer:
$72.9$