In a rectangular triangle [tex]\tan\theta\dfrac{opposite}{adjacent}[/tex].
We have [tex]\tan\theta=\dfrac{3}{4}[/tex]
Therefore opposite = 3uints and adjacent = 4units.
[tex]\csc\theta=\dfrac{hypotenuse}{opposite}[/tex]
We need the length of hypotenuse.
Use the Pythagorean theorem:
[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\to h=5units[/tex]
Substitute:
[tex]\csc\theta=\dfrac{5}{3}[/tex]
