from the top of a tower, the angle of depression of a boat is 30 degree. if the tower is 20 meter high, how far is the boat from the foot of the tower?
sin30/20 = sin60/x
Use soh cah toa to complete the triangle. tan34= h/23
To find the distance from the boat to the foot of the tower, we can use trigonometric ratios.
Given that the angle of depression is 30 degrees and the height of the tower is 20 meters, we are looking for the distance from the boat to the foot of the tower, which we'll denote as "x" meters.
The angle of depression is formed by a horizontal line from the top of the tower to the boat and a line from the top of the tower to the foot of the tower.
If we draw a right triangle with the height of the tower as one side and the distance from the boat to the foot of the tower as the other side, the angle of depression will be the angle between these sides.
In a right triangle, the tangent function relates the opposite side length (the height of the tower) to the adjacent side length (the distance from the boat to the foot of the tower):
tan(angle) = opposite/adjacent
tan(30 degrees) = 20/x
Now, we can solve this equation for x:
x = 20/tan(30 degrees)
Using a calculator, we can find that the tangent of 30 degrees is approximately 0.5774. Therefore:
x = 20/0.5774
x ≈ 34.64
So, the boat is approximately 34.64 meters away from the foot of the tower.