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A civil engineer wants to determine the distances from points A and B to an inaccessible point C in a river. BAC measures 67° and ABC measures 52°. If points A and B are 82.0 feet apart, find the distance from C to each point.
 Jan 29, 2014

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first you find BCA as

BCA=180 - BAC - ABC = 180 - 67 - 52 = 61 deg.

Now you apply the law of sines.

sin(61deg)/82 = sin(52)/AC = sin(67)/BC

so AC = 82*[sin(52deg)/sin(61deg)], BC=82*[sin(67deg)/sin(61deg)]

you can punch the calculator buttons.
 Jan 30, 2014

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