Posted by **Chloe Mack** on Sunday, January 30, 2011 at 7:57pm.

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?

- Pre-Calculus-Trig -
**Henry**, Tuesday, February 1, 2011 at 11:54am
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.

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