SOLUTION: a circular park 80 meters in diameter has a straight path cutting across it. it is 24 meters from the center of the park to the closet point on this path. how long is the path?

Algebra ->  Triangles -> SOLUTION: a circular park 80 meters in diameter has a straight path cutting across it. it is 24 meters from the center of the park to the closet point on this path. how long is the path?      Log On


   

Question 148693: a circular park 80 meters in diameter has a straight path cutting across it. it is 24 meters from the center of the park to the closet point on this path. how long is the path?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
This is a good problem. Analyzing it, that 24 meters from the center of the park to the closest point of this straight path cutting is only possible if it is perpendicular. Draw it on a diagram and you'll see why.
Now that forms two oppposite right triangle, with equal measurements and hypotenuse of each is the radius = 40 meters---- mark "c". Also mark "a" the 24 meters, from the center perpendicular to the middle of the path cutting.
.
Focusing on 1 triangle, we'll get half of the total length of the path cutting then right?---- mark this as highlight%28b%29 ----->unknown oks?
Therefore by Pythagorean Theorem, c%5E2=a%5E2+%2B+b%5E2
b%5E2=c%5E2-a%5E2
b=sqrt%2840%5E2-24%5E2%29
b=sqrt%281024%29
b=32meters
Since that's only 1 triangle showing half of the length, we multiply it by 2 to get the full length of the path cutting, 32meters%2A2=64meters ---> final answer.
Thank you
Jojo