A surveyor notes that the direction from point A to point B is S55°....

Question

A surveyor notes that the direction from point A to point B is S55°W and the direction from A to point C is S24°W. The distance from A to B is 226 yards, and the distance from B to C is 359 yards. Approximate the distance from A to C. PLEASE SHOW HOW TO DO THIS 

 

Answer 1

Angle A =55-24=31 degrees. Not 21 degrees.

 

Rest all the above steps are to be repeated as it is

 

Side AC comes out to be 533.3 yards

Answer 2

Calculate the angle between line AB and line AC.  Both are in the same quadrant, so its just 55 - 24 = 31 degrees, this is angle A.  The side of the triangle opposite angle A is side a = 359 yds.

 

Use Law of Sines.  sin A/a = sin B/b = sin C/c where A, B and C are the angles opposite sides a, b, and c.

 

Let AB = c = 226 yds.

 

Substitute.  sin (31)/359 = sin (C) / 226.  Solve for c.  

 

C = sin^-1( 226 sin (21) / 359) = 18.9 degrees.

 

sum of angles in triangle = 180 --> B = 180 - A - C = 180 - 13 - 21.  Therefore B = 130.1 degrees.  

 

Use the Law of Sines again.

 

sin (A)/a = sin (B)/b where b is distance from A to C.

 

sin (31)/359 = sin (131.1) / b

 

b = 359 sin (131.1) / sin (31) = 526 yds.  (depending on your rounding)