The angle of depression as measured from the top of a 41 foot tower to a reference point on the ground is 65 degrees. How far away, to the nearest foot, is the reference point from the base of the tower?
41/d = tan65°
To find the distance from the base of the tower to the reference point on the ground, we can use trigonometry. The angle of depression is the angle formed by a vertical line from the top of the tower to the reference point and a horizontal line from the top of the tower to the base of the tower.
In this case, the angle of depression is 65 degrees, and the height of the tower is given as 41 feet. We want to find the distance from the base of the tower to the reference point, let's call this distance "x".
We can use the tangent function to find x. The tangent of an angle is equal to the opposite side divided by the adjacent side in a right triangle.
In this case, the opposite side is the height of the tower (41 feet), and the adjacent side is x (the distance we want to find).
Therefore, we have the following equation:
tan(65 degrees) = 41 / x
To solve this equation for x, we can rearrange it as follows:
x = 41 / tan(65 degrees)
Using a calculator, we can find the value of tan(65 degrees) to be approximately 2.1445. Plugging this value into the equation, we get:
x = 41 / 2.1445
Evaluating the right side of the equation, we find:
x ≈ 19.12 feet
Therefore, the reference point on the ground is approximately 19.12 feet away from the base of the tower.