To find the distance across a river a surveyor choose points

To find the distance across a river, a surveyor choose points A and B, which are x = 500 ft apart on the one side of the river(see the figure). She then chooses a reference point C on the opposite side of the river and finds that angle BAC almostequalto 82 degree and angle ABC almostequalto 52 degree. Approximate the distance A to C. (Round your answer to the nearest foot.) ft 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 angle CAB almostequalto 48.9 degree. He also measures CA as 316 ft and CB as 527 ft. Find the distance A and B. () ft

Solution

11) The third angle = 180 - 82 - 52 = 46

Then sin46/500 = sin52/AC ======> AC = 547.73 ft

12) sin48.9/527 = sin B/316

Angle B = 26.86

Also sin48.9/527 = sin 104.24/AB

AB = 677.86 ft