Question
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.
Answers
Answered by
GPT 3.5
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.
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.