we have the following

sin of an angle is the same as:

therefore we can create the following right triangle:
we can calculate the adjacent side using the pythagorean theorem

where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.
thus, the adjacent side is:
![a=\sqrt[]{h^2-b^2}=\sqrt[]{9^2-4^2}=\sqrt[]{81-16}=\sqrt[]{65}](https://img.qammunity.org/2023/formulas/mathematics/college/6cvuljbwdq9fd1h7pgq6oxh7cxbs3ijz10.png)
Using that value, we can now calculate cos of the angle

![\cos \theta=\frac{\sqrt[]{65}}{9}](https://img.qammunity.org/2023/formulas/mathematics/college/tueiia4vgmg9bo5dr9i62ydid6nwwbqe49.png)
which can't be simplify, thus that is the answer for the exact value