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?.
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.
To find the distance between the boat and the foot of the tower, we can use trigonometry, specifically the tangent function.
Let's assume the distance between the boat and the foot of the tower is represented by "d" meters.
We can set up the following equation using the tangent function:
tan(30 degrees) = opposite / adjacent
In this case, the opposite side is the height of the tower (20 meters) and the adjacent side is the distance between the boat and the foot of the tower (d meters).
Using the known value for the angle of depression:
tan(30 degrees) = 20 / d
Now, we can solve this equation for "d" to find the distance between the boat and the foot of the tower.
Start by taking the tangent of 30 degrees:
tan(30 degrees) ≈ 0.577
Simplifying the equation further:
0.577 = 20 / d
To isolate "d", we can cross multiply:
0.577d = 20
Now, divide both sides of the equation by 0.577 to solve for "d":
d ≈ 20 / 0.577
Calculating this value yields:
d ≈ 34.64
Therefore, the boat is approximately 34.64 meters away from the foot of the tower.
To find the distance from the boat to the foot of the tower, we can use trigonometry. Specifically, we can use the tangent function, as the angle of depression is given.
Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the tower (20 meters) and the angle of depression is 30 degrees.
Let's label the distance we are trying to find as 'x'. In the right triangle formed by the tower, the horizontal distance from the foot of the tower to the boat (adjacent side) is 'x'. The height of the tower (opposite side) is given as 20 meters.
Using the tangent function, we have:
tan(30 degrees) = opposite/adjacent
tan(30 degrees) = 20/x
To solve for 'x', we can rearrange the equation:
x = 20/tan(30 degrees)
Now, we can calculate the value by plugging in the values:
x = 20/tan(30 degrees)
x ≈ 34.64 meters
Therefore, the boat is approximately 34.64 meters away from the foot of the tower.