Question

A surveyor stakes out points A and B on sides of a building. Point C on the side of the building is 300 feet from A and 440 feet from B. Angle ACB measures 38 degrees. What is the distance from A to B?

Answer 1

Use the Law of Cosines to solve triangle ABC:

cosC = (a^2 + b^2 - c^2) / 2ab.

cos38=((440)^2+(300)^2-c^2)/2*440*300,
0.7880 = (283600 - c^2) / 264000,
Cross multiply:
-c^2 + 283600 = 208032,
-c^2 = 208032 - 283600,
-c^2 = - 75568,
c^2 = 75568,
c = 275ft. = Distance from A to B.