A blimp provides aerial television views of a football game. The television camera sights the stadium at a 7° angle of depression. The altitude of the blimp is 400 meters. Which of the following is the line-of-sight distance from the television camera to the base of the stadium? Round to the nearest meter. (1 point) Responses 403m 3,257m 3,282m 4,500m
To determine the line-of-sight distance from the television camera to the base of the stadium, we can use trigonometry.
Given:
Angle of depression = 7°
Altitude of blimp = 400 meters
Let x be the distance from the camera to the base of the stadium.
Using the tangent function:
tan(7°) = 400/x
x = 400/tan(7°)
x ≈ 400/0.12217
x ≈ 3267.19 meters
Rounded to the nearest meter, the line-of-sight distance from the television camera to the base of the stadium is 3,267 meters.
Therefore, the closest option is 3,257m.