SOLUTION: Please help me solve this trigo problem. Two roads intersect at an obtuse angle. Two points are chosen:X, 0.12 mi from the intersection, and Y, 0.24 mi from the intersection. If t

Question 96839: Please help me solve this trigo problem.
Two roads intersect at an obtuse angle. Two points are chosen:X, 0.12 mi from the intersection, and Y, 0.24 mi from the intersection. If the line of sight from X to Y makes an angle of 52 degrees with one road at point X, what is the measure of the obtuse angle between the roads?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two roads intersect at an obtuse angle. Two points are chosen:X, 0.12 mi from the intersection, and Y, 0.24 mi from the intersection. If the line of sight from X to Y makes an angle of 52 degrees with one road at point X, what is the measure of the obtuse angle between the roads?
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Draw the picture. Label X,Y and let the obtuse angle be labeled "Z".
You are given the length of two sides:
x=0.12 , y=0.24
You are given the angle X = 52 degrees
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Use the Law of Sines to find angle Y:
sin Y/0.12 = sin 52/0.24
sin Y = 0.12[sin 52/0.24] = 0.39400...
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Find anti-sin (0.39400...) = 23.204 degrees
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Then angle Z = 180-52-23.24 = 104.796... degrees
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Cheers,
Stan H.
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