To solve this problem, we can use trigonometry, specifically the concept of angles of depression.
a) To find the angle of depression of the foot of the pole from the woman, we need to find the angle between the line of sight from the woman to the foot of the pole and the horizontal.
Let's assume the angle of depression of the foot of the pole from the woman is θ degrees. Since the angle of depression of the flag pole is given as 44°, we can use the fact that the angle of depression and angle of elevation are congruent when looking at the same object.
Therefore, θ = 44°.
b) To find the height of the flag pole, we can use the tangent function.
Let h be the height of the flag pole.
In the triangle formed by the woman, the foot of the pole, and the top of the pole, the opposite side is the height of the pole (h), the adjacent side is the horizontal distance between the foot of the pole and the woman (25m), and the angle θ is 44°.
Using the tangent function:
tan θ = opposite/adjacent
tan 44° = h/25
Rearranging the equation to solve for h:
h = tan 44° * 25
Using a calculator, the approximate value of h is 29.47 meters.
Therefore, the height of the flag pole is approximately 29.47 meters.