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

From the description

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

Answer (approximately): 150.26 degrees

Just for walking in the door, before any lessons,

Celeste . . . $5.00
Dora. . . . . $10.25

For 'H' hours of instruction,

Celeste . . . $7.25 x H
Dora . . . . . $6.50 x H .

Total cost to take lessons from

Celeste . . .  5 + 7.25H
Dora . . . . . 10.25 + 6.5 H

What is the number of hours ' H ' when both of their total costs
would be the same ?

5 + 7.25H = 10.25 + 6.5H

Subtract  6.5H  from each side:  5 + 0.75H = 10.25

Subtract  5  from each side:  0.75H = 5.25

Divide each side by  0.75 :      H = 5.25/0.75  =  7 hours 

After 7 hours of instruction, Celeste's student and Dora's student
have both paid $55.75 .  After that, Celeste's student pays 75¢
more for each hour of instruction than Dora's student pays.