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A surveyor notes that the direction from point A to point B is S57°W and the direction from A to point C is S36°W. The distance from A to B is 219 yards, and the distance from B to C is 378 yards. Approximate the distance from A to C.

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Shinalcantaraviz
Please refer to the illustration below.
Use cosine law to find the distance AC 
BC² = AC² + AB² - 2(AC)(AB)cosA
378² = AC² + 219² - 2(AC)(219)cos21
AC² - 2(AC)(219)cos21 +219² - 378² = 0
AC² - 408.908AC - 94,923 = 0
AC = 574.217; AC = -165.309
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Take the positive value
Therefore the approximate distance of AC is 574.217 yards.
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