you are standing on one side of the river. Figure out the width of the river. All calculations have to be made on the side you are standing on. You cant step into the river or cross it. You may use the 2 laws ( sine and cos ). no guessing allowed. has to be accurate.

Answer 1

You know how high you are. You know or can measure the angle downward from the horizontal to the opposite side (use some sort of survey telescope, but you have to determine that angle.)

You then can easily determine it. You know one side, and an angle.
Tangent would be nice, and tangent is just your height/width. and you solve for width.
There is another way, more difficult.

Answer 2

i don't understand what you mean , simpler terms?

Answer 3

draw the triangle from a point on the opposite shore to your feet, then one leg up, your height. You measure the depression angle from the horizon to the point on the other shore. So in the triangle, that is the same angle at the base of the triangle on the other side.
Tan angle= your height/width