SOLUTION: 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?

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

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