From the top of a tower the angle of depression of a boat is 30degree if the tower is 20m height,how far is the boat from the foot of the tower
Make your diagram to see that you have a right-angled triangle
with a base angle of 30° and opposite side of 20 m.
you want the adjacent, so clearly the tangent ratio is needed
tan 30° = 20/x
x = 20/tan30° = ??? m
To find the distance of the boat from the foot of the tower, we will use trigonometry.
Given:
Height of the tower (opposite side) = 20 m
Angle of depression = 30 degrees
Let's label the distance from the foot of the tower to the boat as 'x'.
In a right-angled triangle, the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, the tangent of the angle of depression is equal to the height of the tower divided by the distance 'x' between the tower and the boat.
So, we have:
tan(30 degrees) = 20 m / x
Now, let's solve for 'x':
x = 20 m / tan(30 degrees)
Using a calculator:
x ≈ 34.64 m
Therefore, the boat is approximately 34.64 meters away from the foot of the tower.
To find the distance from the foot of the tower to the boat, we can use trigonometry. In this case, we can use the tangent function.
The angle of depression is the angle between the line of sight from the top of the tower to the boat and the horizontal.
Given:
- Height of the tower (opposite side) = 20m
- Angle of depression = 30 degrees
Let's label the distance from the foot of the tower to the boat as "x."
Using the tangent function, we have:
tan(angle of depression) = opposite side / adjacent side
tan(30 degrees) = 20m / x
To find x, we can rearrange the equation:
x = 20m / tan(30 degrees)
Using a calculator, we can evaluate the tangent of 30 degrees as approximately 0.5774:
x = 20m / 0.5774
Simplifying the equation, we find:
x ≈ 34.64 meters
Therefore, the boat is approximately 34.64 meters from the foot of the tower.