If the cosine of the angle is 3/4, draw a right-angled triangle with sides 3, $\displaystyle \sqrt{7}$ and hypotenuse 4. This satisfies the Pythagorean Theorem. The 4 is given in the problem, $\displaystyle \sqrt{7}$ is the calculated value for the side that is not given. Now the tangent would be (opposite side/adjacent side) = $\displaystyle \sqrt{7}$/3. The sine would be the opposite side divided by the hypotenuse.
Is this what you are asking?
no, i would like to see how one goes about solving what i attached, the tangent theta = square root 15. i do not know where the four comes from. also, if a formula could be provided for how one solves the problem i attached. i only mentioned cosine 3/4 to show i understand how to do these types of problems regarding cosines.