An advertising blimp hovers over a stadium at an altitude of 125 m. The pilot sights a tennis court at an 8o angle of depression. To the nearest meter, find the ground distance in a straight line between the stadium and the tennis court.
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To solve this problem, we can use trigonometry. Let's denote the ground distance between the stadium and the tennis court as "d."
Using the given information, we can set up a right triangle. The angle of depression is 8 degrees, the side opposite the angle is 125 m (height of the blimp), and the side adjacent to the angle is "d" (ground distance).
To find the ground distance "d," we can use the tangent function:
Tan(angle) = opposite / adjacent
Tan(8 degrees) = 125 m / d
To find "d," we need to isolate it. Rearrange the equation:
d = 125 m / tan(8 degrees)
Using a calculator, calculate tan(8 degrees):
Tan(8 degrees) ≈ 0.1405
Now substitute this value back into the equation:
d ≈ 125 m / 0.1405
d ≈ 890.46 m
To the nearest meter, the ground distance between the stadium and the tennis court is approximately 890 meters.
To find the ground distance between the stadium and the tennis court, we can use the concept of trigonometry, specifically the tangent function.
First, let's draw a diagram to visualize the situation. We have an advertising blimp hovering over the stadium at an altitude of 125 m. The pilot sights the tennis court and forms an angle of depression, which is the angle between the pilot's line of sight and the horizontal ground.
We know that the angle of depression is given as 8 degrees. Let's denote the ground distance between the stadium and the tennis court as 'x' meters.
Now, we can use the tangent function, which relates the angle of depression to the ratio of the opposite side (altitude of the blimp) to the adjacent side (ground distance).
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the tangent of the angle of depression can be written as:
tan(8 degrees) = 125 / x
To find the value of 'x', we can rearrange the equation:
x = 125 / tan(8 degrees)
Now we can calculate the value of 'x' using a calculator:
x = 125 / tan(8 degrees) ≈ 878.19 meters
Therefore, to the nearest meter, the ground distance between the stadium and the tennis court is approximately 878 meters.