QUESTION 1
The tangent ratio is the ratio of the length of the opposite side to the length of the adjacent side.
![\tan(M) = (LN)/(NM)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/smdx7z8eb102r9wuxnffyp3k3jdewamw2z.png)
![\tan(M) = (8)/(6) = (4)/(3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/vc51tzvhyiwvhblyl5vbuiwrd751f3z7yo.png)
QUESTION 2.
We again use the tangent ratio to find angle S.
![\tan(S) = (TU)/(SU)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/flf9se9mwibwg7d0vtuj0xod8d80nk9hrh.png)
![\tan(S) = (0.75)/(3.5)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nwsqeaccf8bn64tuuydm3cm7uc3u04mlx0.png)
![\tan(S) = (3)/(14)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/579p493s130jb5bi3asn7uh5f8mlbzb5ph.png)
![S = { \tan}^( - 1) ( (3)/(14) )](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xdfqnahixcxggircj63hdjx5tu3tlsx672.png)
![S = 12.09 \degree](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uzwcrfezyv5tf1gyot3ewj0hse93sm4nas.png)
to the nearest hundredth.
QUESTION 3
We can find CE using the tangent ratio.
![\tan(27 \degree) = (18)/(CE)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lkxpuqjjypkg6hv89oqrevd9hcxa0jxjun.png)
![CE = (18)/( \tan(27 \degree) )](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7kdlnq94eopdros0vhj7fw7gicp7bdw9ro.png)
![CE = 35.3 \degree](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4d6uyaknkisuu4wr2bf6zr9ywebz82134l.png)
to the nearest 0.1.