Question

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

Answer 1

From the description

`\tan \angle AOB = \frac 4 7`

`\angle AOB = \arctan \frac 4 7 \approx 29.74^\circ`

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

`\angle A'OB = 180^\circ - 29.74^\circ = 150.26^\circ`

Answer (approximately): 150.26 degrees