Let's denote the distance from the top of the tower to the boat as "x" meters. Since the angle of depression is 30 degrees, we can use trigonometry to solve for "x".
In a right triangle, the tangent function is defined as the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the tower (20 meters) and the adjacent side is the distance from the foot of the tower to the boat (x meters).
Tangent(30 degrees) = Opposite/Adjacent
tan(30°) = 20/x
Using a scientific calculator, we can determine that the tangent of 30 degrees is approximately 0.5774.
0.5774 = 20 / x
Solving for "x", we can multiply both sides of the equation by "x":
0.5774x = 20
Dividing both sides by 0.5774:
x ≈ 20 / 0.5774
x ≈ 34.64
Therefore, the distance from the foot of the tower to the boat is approximately 34.64 meters.
From the top of the tower the angle of depression is 30 degrees if the tower is 20 meters high . how far is the boat from the foot of the tower?.
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