Using SOH CAH TOA, we know that we can find the measure of angle A by using either sin or tan. We’ll go with sin, which is opposite over hypotenuse.
The side opposite of angle A is BC, so the numerator will be 4. The side across from the 90 degrees of angle B is AC, so our denominator is 5.
Now that we have the amount of (4/5), we have to do the inverse of sin to find the angle measure. You use a scientific calculator and put in 2nd, sin (4/5), which gives you .927.
Therefore, your answer is 92.7 degrees.