Points A and B are separated by a lake.

Question

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 = 48.1°. He also measures CA as 311 ft and CB as 527 ft. Find the distance between A and B. (Round your answer to one decimal place.)

Answer 1

Use the law of sines to get angle ABC.

Then remember that the sum of the angles of a triangle is 180 degrees to get angle ACB.

Then use either the law of cosines or the law of sines to get the length of AB,