Trying to find theta in a right triangle

Question

There is a right triangle, ΔABC, where ∠C is the right angle, making AB the hypotenuse. There is altitude CD drawn to the hypotenuse, thus forming ΔACD and ΔCBD, similar to each other and the original triangle, ΔABC. The hypotenuse of ΔABC is 4 units and altitude CD is 1 unit. ∠ABC is labeled as θ, AD as x, DB as 4-x, CB as a, and AC as b. We are trying to find θ.

I have managed to find the value of x, by setting up the equation (x/1)=(1/(4-x)), and getting the values x=2±√3. Both could work getting that θ=75° and 15°. How would I know which one to use? Is this work even correct?

Answer 1

If m∠B = 75°, then m∠A = 15°, and conversely if m∠A = 75° then m∠B = 15°.