If you know two sides of a triangle, trig lets you find the third. So if you want to know the distance across a lake, measure two lines along the side of the lake such that they form a triangle with the line across the lake, and you can find the distance across.
You can also find one side if you know one side and the angles at either end. This can be used to find the heights of objects - you know the angle it makes to the ground, how far you are from it, and what angle you have to look at to see the top.