trigonometry (oblique triangle) A surveyor wants to find the distance from point A on one side of a small lake from a vantage point C he measures two distances AC=325m and BC=235m. He also measures the angle between AC and BC to be 52'40'. What is the distance from A to B?

So, $\angle ACB=52'40''$
Applying the Law of Cosines,
$$\cos 52'40''=\frac{AC^2+BC^2-AB^2}{2\cdot AC\cdot BC}\iff AB^2=AC^2+BC^2-2\cdot AC\cdot BC\cdot \cos 52'40''$$
