You have triangle ABC with B the right angle. You are told there is a bridge across a chasm 30 m wide and that is at side AB. You are told the bridge is "20 degrees from the horizontal". Since The chasm, side AB, is "horizontal", it is angle A that is 20 degrees. And the height of the bridge, in going from one side to the other is the length of side BC.
First, you have 3m in the wrong place. The way you have drawn it, B is the right angle. 3m is the length of the hypotenuse and that is always the side opposite the right angle (the longest side in a right triangle). Once that is done, you are free to put the 30 degrees at either A or C because which is the "near side" and which is the "opposite side" will depend upon where you put the angle.
If you choose to put the 30 degrees at angle A, then BC is the "opposite side" and AB is the "near side". If you choose to put the 30 degrees at angle C, then BC is the "near side" and AB is the "opposite side".
Those two different choices for where to put the 30 degrees angle will give different answers for the length of AB and BC but the same answers for "near side" and "opposite side".