A 50-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What is the angle of depression from the top of the tower to the point on the ground where the cable is tied?
To solve this problem, we can use the tangent function.
Let's call the angle of depression θ.
Tangent is the ratio of the opposite side (the height of the tower) to the adjacent side (the distance from the tower to where the cable is tied).
So we have:
tan θ = opposite/adjacent
tan θ = 50/30
Now we can use a calculator to find the inverse tangent (tan^-1) of this ratio:
θ = tan^-1(50/30)
θ ≈ 59.04 degrees
Therefore, the angle of depression from the top of the tower to the point on the ground where the cable is tied is approximately 59.04 degrees.