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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?

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please add your ideas/work and where you struck. –  Ram Jan 20 '13 at 10:07
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1 Answer

So, $\angle ACB=52'40''$

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

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so how can i draw a diagam from that problem...pls...answer –  yoj Jan 20 '13 at 10:08
oh i cant get it...the problem is the surveyor will try to find angle AC do you mean i will draw a lake that would create a oblique...thank you.. –  yoj Jan 20 '13 at 10:51
@yoj, we have two options : (1)Draw $52′40′′$ which can not be ruler-and-compass construction, make its container sides AC=325 & BC=235 unit. Join AB. (2) Once you have side $|AB|$ known, its not tough to draw a triangle with all the three sides known. –  lab bhattacharjee Jan 20 '13 at 14:38
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