Compute the distance between points a and b

Question

  To compute the distance between two points  and , a surveyor chooses a point  that is 300 yards from  and 500 yards from B.  The surveyor measures the angle  as .  The angle  is a right angle (i.e. ).  Compute the distance between points a  and  b  

 

Answer 1

The point the surveyor chose is 300 yards from A and 500 yards from B.

 

To picture this, imagine the surveyor standing at a corner.  Point A is 300 yards to the right and Point B is 500 yards straight ahead.

 

Since this is a right angel, we know the following relationship between the length of the sides.

a² + b² = c²

where a² and b² are the lengths of the 2 sides squared and c² is the length of the distance between the two points, A and B, squared.

 

300² + 500² = c²

90000 + 250000 = c²

340000 = c²

c = √340000 = 100√34 = distance between points A and B.