A point on a bridge across a river is 4 m above the two banks. From that point the angles of depression of the banks on opposite sides are 30° and 45°. The width of the river is:

The horizontal distances to the two banks are 4·cot30° = 4√3 and 4·cot45° = 4. Because the banks lie on opposite sides, the width is the sum 4√3 + 4 = 4(√3 + 1) ≈ 10.93 m — subtracting would be the mistake for banks on the same side.