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)
403 m
3,257 m
3,282 m
4,500 m
To find the line-of-sight distance from the camera to the base of the stadium, we can use the trigonometric relationship of tangent.
In this case, the angle of depression is given as 7° and the altitude of the blimp is 400 meters.
The tangent of an angle is defined as the opposite side divided by the adjacent side. In this case, the opposite side is the height of the blimp (400 meters) and the adjacent side is the line-of-sight distance.
So, we can set up the equation:
tangent(7°) = 400 / x
To solve for x (the line-of-sight distance), we can rearrange the equation:
x = 400 / tangent(7°)
Using a calculator, we find:
x ≈ 3206.3 meters
Rounded to the nearest meter, the line-of-sight distance from the television camera to the base of the stadium is 3,206 meters.
Therefore, the correct answer is 3,257 m.