From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34*. How far is the object from the base of the cliff?
Let's call the distance from the base of the cliff to the object "x".
The angle of depression is the angle between the line of sight from the top of the cliff to the object and the horizontal line. So, the angle of depression is 34 degrees.
We can use trigonometry to find the value of x.
In a right triangle formed by the cliff, the line of sight from the top of the cliff to the object, and the horizontal line, the height of the cliff is the opposite side, and x is the adjacent side.
We can use the tangent function to find x:
tan(angle of depression) = opposite/adjacent
tan(34 degrees) = 40/x
We can solve this equation for x.
x = 40/tan(34 degrees)
x ≈ 40/0.675 = 59.26
So, the object is approximately 59.26 meters from the base of the cliff.