Question 271789: Approximate the length by finding the necessary arc length.
A television tower 440m high subtends an angle of 5degrees 50'. How far away is the tower?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! television tower is 440 meters high.
5 degrees 50 minutes is roughly equivalent to an angle of 5.83333333 degrees.
5.833333333/360 * 2 * pi * r = the arc length of this angle.
that would be equal to .101810872 * r
if we assume the arc length and the height of the tower are approximately equal, then .101810872 * r = 440
solving for r, we get r = 440/.101810872 = 4321.738822 meters.
that's about how far the television tower is from the observer.
since the arc length is going to be a little longer than the length of the chord formed by the flagpole, this means that the distance of 4321.738822 meters is going to be a little less than the actual distance.
for example, assume the arc length is 450 meters.
then the radius would be equal to 450/.101810872 = 4419.960159 which is slightly longer.
I couldn't find a way to get the arc length exactly without knowing the radius.
here's a definition of what subtending angle means.
http://www.mathopenref.com/subtend.html
|
|
|
