Final answer:
The ground distance between the stadium and the tennis court can be calculated using trigonometry, given the altitude of the blimp is 125m and the angle of depression is 8 degrees. The ground distance is found to be approximately 889.68 meters.
Step-by-step explanation:
To find the ground distance between the stadium and the tennis court, we need to use the concept of angles of depression and trigonometry.
First, we know that the angle of depression from the blimp to the tennis court is 8 degrees. This angle is congruent to the angle of elevation from the horizontal ground to the blimp when viewed from the tennis court due to alternate interior angles created by a transversal (the line of sight from the blimp) across two parallel lines (the horizontal ground and the line parallel to it through the blimp).
Given the altitude of the blimp is 125m, and the angle of elevation is 8 degrees, we are dealing with a right triangle where the altitude is the opposite side, and the ground distance we need to find is the adjacent side. To solve for the adjacent side, we'll use the tangent function:
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
So, tan(8 degrees) = opposite/adjacent, which rearranges to adjacent = opposite/tan(8 degrees).
Substituting the given values leads to adjacent = 125m / tan(8 degrees).
Using a calculator, we find that tan(8 degrees) is approximately 0.1405, so the ground distance is 125m / 0.1405 ≈ 889.68 meters.
Therefore, the ground distance between the blimp and the tennis court is approximately 889.68 meters.