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in a right angled triangle OAB, OB:AB=7:4 and OA is the longest side of the triangle. Triangle OAB is rotated about the point O to form trriangke OA'B' such that AOA' is a straight line. Find obtuse angle A'OB

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DeanR

From the description


[tex] \tan \angle AOB = \frac 4 7[/tex]


[tex] \angle AOB = \arctan \frac 4 7 \approx 29.74^\circ[/tex]


If we rotate so AOA' is straight, that's a 180 degree rotation. So A'OB is the supplement of the above,


[tex] \angle A'OB = 180^\circ - 29.74^\circ = 150.26^\circ [/tex]


Answer (approximately): 150.26 degrees



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