In the given right triangle
Applying the Pythagorean Theorem
Find out the vertical leg (y)
[tex]\begin{gathered} 8^2=3^2+y^2 \\ y^2=8^2-3^2 \\ y^2=55 \\ y=\sqrt{55} \end{gathered}[/tex]
Find out the cotθ
[tex]cotθ=\frac{3}{\sqrt{55}}[/tex]
Simplify
[tex]cotθ=\frac{3\sqrt{55}}{55}[/tex]
Find out the sinθ
[tex]sinθ=\frac{\sqrt{55}}{8}\text{ ----> by SOH}[/tex]
Find out cscθ
cscθ=1/sinθ
[tex]cscθ=\frac{8}{\sqrt{55}}[/tex]
Simplify
[tex]cscθ=\frac{8\sqrt{55}}{55}[/tex]
