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.

For practical purposes, divide all values by 4.5 (the radius of the circle).  We now have a circle with radius 1.  The first point lies along the north-south axis while the second point lies along the east-west axis.  The intermediary point on the circumference forms an angle relative to the east-west axis.  The sine of this angle equals the opposite side, 1/3 ( 1.5/4.5).  Using trig, the angle equals 19.47123 degrees.  The cosine of this angle will equal the distance between A and the intermediary point.  Now with two sides of a right triangle, the Pythagorean theorem is used to calculate the distance between A & B.

√[(1/3)² + (0.812905)²] = 0.878593056

Multiply this by 4.5 and you get:

3.953668751

Posted by hoodat on 2010-08-31 16:21:03