Final answer:
To find the height of the pole using the angles of depression of 45° and 60°, trigonometry is applied and the two equations set up lead to a calculation which gives the height of the pole as approximately 16.4 meters.
Step-by-step explanation:
The student is asking about finding the height of a pole based on the angles of depression observed from the top of a tower. To solve this, we can use trigonometry. The tower is 50 meters high, and from that height, the angles of depression to the top and bottom of the pole are 45° and 60°, respectively.
Let's name the height of the pole 'h' and the horizontal distance between the base of the tower and the pole 'd'. Using the tan function for the 45° angle, we get tan(45°) = h / d = 1, which means the height of the pole is equal to the distance 'd' (h = d). For the 60° angle, we get tan(60°) = (50 - h) / d = √3. Solving these two equations together gives us the height 'h' of the pole.
By doing the math, we find the height of the pole h = 50(√3 - 1) / (√3 + 1), which calculates to be approximately 16.4 meters.