Points A and B are separated by a lake To find the distance

Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that CAB = 48.2°. He also measures CAas 313 ft and CB as 527 ft. Find the distance between A and B. (Round your answer to one decimal place.)
  ft

Solution

Use sine rule:

a/sinA = b/sinB

side opposite to Angle CAB is CB

CB/sinCAB = CA/sinCBA

sinCBA = 313*sin48.2/527 = 0.4427

Angle CBA = 26.28 deg

Angle ACB = 180 - 48.2 - 26.28 = 105.52 deg

apply sine rule:

AB/sin105.52 =CB/sinCAB

AB = 527*sin105.52/sin48.2 = 681.15 = 681.2ft