Answer: If you know the angle of depression from a point to an object and the height of the point above the horizontal plane, you can use trigonometry to find the horizontal distance to the object. The angle of depression is the angle formed by a horizontal line from the observer to the object and the line of sight from the observer to the object.
Here are the steps to find the horizontal distance when the angle of depression is given:
Draw a diagram to represent the problem. Mark the point of observation, the object being observed, and the horizontal line passing through the point of observation.
Identify the angle of depression in the diagram.
Use trigonometry to find the vertical distance (height) between the point of observation and the object. The vertical distance is equal to the difference between the height of the observer and the height of the object.
Use trigonometry again to find the horizontal distance between the point of observation and the object. The horizontal distance is equal to the vertical distance divided by the tangent of the angle of depression.
Here is the formula to find the horizontal distance:
Horizontal distance = Vertical distance / tan(angle of depression)
In symbols, this can be written as:
D = h / tan(theta)
where D is the horizontal distance, h is the vertical distance, and theta is the angle of depression.
Make sure that the units of height and distance are the same and that the angle is measured in the same units as the tangent function expects (radians or degrees).
Explanation: