A surveyor notes that the direction from point A to point B

A surveyor notes that the direction from point A to point B is S63 degree W and the direction from A to point C is S38 degree W. The distance from A to B is 226 yards, and the distance from B to C is 369 yards. Approximate the distance from A to C. 560 yd 561 yd 563 yd 558 yd

Solution

Solution:

Angle A = 63-38 = 25⁰

By using sin function

sin C/c = sin A/a

sin C/226 = sin (25/369)

sin C = (sin 25*226) / 369

sin C = 0.2640

C = 15.3075411085

angle C = 15.31⁰

25 +15.31 = 40.31

180 - 40.31 = 139.69

angle B = 139.69 degrees

b/sin B = a/ sin A

b/sin 139.69 = 369/ sin 25

b = (sin 139.69*369) / sin 25

b = 561.24 (to 2 d.p.)

distance A to C = 561 yards.