To find the line-of-sight distance, we can use trigonometry.
First, we need to find the horizontal distance between the television camera and the base of the stadium.
We can use the tangent function:
tan(8 degrees) = opposite/adjacent
tan(8 degrees) = height of blimp/horizontal distance
horizontal distance = height of blimp / tan(8 degrees)
horizontal distance = 500 / tan(8 degrees)
horizontal distance ≈ 3484.88 meters
Now, to find the line-of-sight distance:
line-of-sight distance = √(horizontal distance^2 + altitude^2)
line-of-sight distance = √(3484.88^2 + 500^2)
line-of-sight distance ≈ √(12129934 + 250000)
line-of-sight distance ≈ √12379934
line-of-sight distance ≈ 3516.56 meters
Therefore, the line-of-sight distance from the television camera to the base of the stadium is approximately 3517 meters.
A blimp provides aerial television views of a football game . The television camera sights the stadium an 8 degrees angle of depression. The altitude of the blimp is 500 m. What is the line-of-sight distance (hypotenuse) from the television camera to the base of the stadium? Round your answer to the nearest meter.
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