the angle of depression from the top of a building to a point on the ground is 32degrees30', how far is the point of the ground from the top of building if the building is 252m high?
To find the distance from the point on the ground to the top of the building, we can use trigonometry. The angle of depression is the angle between the horizontal line and the line of sight from the top of the building to the point on the ground.
We can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle.
In this case, the opposite side is the height of the building (252 meters), and the adjacent side is the distance we want to find (let's call it 'x').
Using the formula for the tangent of an angle:
tan(angle) = opposite / adjacent
tan(32°30') = 252 / x
To solve for x, we'll rearrange the equation:
x = 252 / tan(32°30')
Now, we can calculate the value of x using a calculator:
x ≈ 252 / tan(32°30') ≈ 252 / 0.6477 ≈ 389.2 meters
Therefore, the point on the ground is approximately 389.2 meters away from the top of the building.