from the top of a tower, the angle of depression of a boat is 30.if the tower is 20m high ,how far is the boat from the foot of the tower
Let "x" be the distance from the foot of the tower to the boat.
Since the angle of depression from the top of the tower is 30 degrees, we can form a right triangle with the tower, the distance from the foot of the tower to the boat, and the line of sight from the top of the tower to the boat.
In this triangle, the opposite side is the height of the tower (20m) and the angle opposite the side is 30 degrees.
We can use the trigonometric ratio for tangent to find the distance "x" from the foot of the tower to the boat:
tan(30) = opposite side / adjacent side
tan(30) = 20 / x
x = 20 / tan(30)
x ≈ 20 / 0.5774
x ≈ 34.64 meters
Therefore, the boat is approximately 34.64 meters away from the foot of the tower.