How far apart are A and B (to the nearest yard)?

Question

Two points A and B are on opposite sides of a building. A surveyor chooses a third point C 76 yd from B and
102 yd from A,  with angle ACB measuring 55.6°.  How far apart are A and B (to the nearest yard)?

Answer 1

This is a straight forward use of the law of cosines; you have 2 sides and the included angle of a triangle.

 

The formula is c² = a² + b² -2ab cos ∠C, where for your problem a =76, b = 102 and ∠C = 55.6°.

 

Plug in the values...your graphing calculator or a spreadsheet will have the cos function and the square root function.