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 = 48.6°. He also measures CA as 310 ft and CB as 527 ft. Find the distance between A and B. Round your answer to the nearest foot. (Note: ABC is an acute angle.)

Answer 1

Use the Law of Cosine

`c^2=a^2+b^2-2abcos(\gamma)`


`527^2=310^2+AB^2-2*310* AB*cos(48.6^o) \\AB^2-410* AB-181,629=0 \\ \\AB= (410+ √(410^2-4(-181629)) )/(2) =678`