[Guest]

A circular park has a diameter of 9 km.

Monument A is located by entering the park from the northern most point and proceeding due south for 3 km. Starting at the monument A and going due west you would eventually reach the edge (circumference) of the park.

At that point, if you go due south for 1.5 km, you would reach the monument B.

Determine the distance between monument A and monument B.

[Guest]

I get square root of 31.5;

[Guest]

4.5 km.

We went a total distance due south of 4.5 km. This happens to be the same as a radius of the park, so if we go due east from B, we will be moving along a diameter of the circle, perpendicular to our original path. This means that points A, B, and the place where we hit the edge of the park are on a rectangle, with a diagonal equal to the radius. A and B happen to define the other diagonal of this rectangle, so the answer is 4.5 km.

[Guest]

4.5 km.

We went a total distance due south of 4.5 km. This happens to be the same as a radius of the park, so if we go due east from B, we will be moving along a diameter of the circle, perpendicular to our original path. This means that points A, B, and the place where we hit the edge of the park are on a rectangle, with a diagonal equal to the radius. A and B happen to define the other diagonal of this rectangle, so the answer is 4.5 km.

Silly me, no wonder I thought the problem seemed odd. I took the distance from B to a different point than A.

Nice diagram Chuck.

[Guest]

hypotenuse of the rt angle triangle(AB & the center) 4.5 km

Edited February 28, 2010 by Me&MyBrain

[Guest]

Answer - 4.5 km

The radius of the circle is 4.5

The hypotenuse of the rectangle created by following the stated directions is also 4.5, which is the distance from point A to point B.