trigonometry test

Question

The straight-line distances between three different buildings form a triangle. Building A is 143.3 m from building B. Building B is 259.8 m away from building C. The angle at building A is 69°. 

Draw a diagram of the situation (send in by email). How far apart are buildings A and C?

Answer 1

Use the law of cosines

AC^2 = AB^2 + AC^2 -2(AB)(AC)cos(angle opposite AC)

AC^2 = (259.8)^2 + 143.3^2 - 2(259.8)(143.3)cos69

then take the square root