Question

Using the law of cosines, in triangle RST, if r=14 yd, s=9 yd, t=16 yd find m angle s

Help? Thank you

Answer 1

10.05 I’m pretty sure

Answer 2

check the picture below.


`\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = √(a^2+b^2-(2ab)cos(C)) \\\\\\ \cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^(-1)\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\ -------------------------------`


`\bf s^2=r^2+t^2-2rt\cdot cos(S)\implies s^2-r^2-t^2=-2rt\cdot cos(S) \\\\\\ \cfrac{s^2-r^2-t^2}{-2rt}=cos(S)\implies \cfrac{r^2+t^2-s^2}{2rt}=cos(S) \\\\\\ cos^(-1)\left( \cfrac{r^2+t^2-s^2}{2rt} \right)=\measuredangle S\implies cos^(-1)\left( \cfrac{14^2+6^2-9^2}{2(14)(6)} \right)=\measuredangle S`

make sure your calculator is in Degree mode if you need ∡S in degrees.