We first need to calculate the missing side of the triangle. We can do that by applying Pithagora's theorem as shown below:
[tex]\begin{gathered} 20^2=10^2+x^2 \\ x^2=400-100 \\ x^2=300 \\ x=17.32 \end{gathered}[/tex]We can now calculate the trigonometric figures. We will start by the sine.
[tex]\begin{gathered} \sin \theta=\frac{oposite\text{ side to the angle }\theta}{\text{hypothenuse}}=\frac{17.32}{20}=0.866 \\ \end{gathered}[/tex]We can then calculate the cosecant:
[tex]\text{ cossec }\theta=\frac{1}{\sin \theta}=\frac{1}{0.866}=1.155[/tex]We will then calculate the cosine.
[tex]\cos \theta=\frac{\text{ adjacent side to the angle }\theta}{\text{hypothenuse}}=\frac{10}{20}=0.5[/tex]We can calculate the secant:
[tex]\sec \theta=\frac{1}{\cos \theta}=\frac{1}{0.5}=2[/tex]We will then calculate the tangent:
[tex]\tan \theta=\frac{\text{ opposite side to the angle }\theta}{\text{ adjacent side to the angle }\theta}=\frac{17.32}{10}=1.732[/tex]We can now calculate the cotangent:
[tex]\text{ cot }\theta=\frac{1}{\tan \theta}=\frac{1}{1.732}=0.577[/tex]