I need help on this question.
I was thinking of counting the area of the whole circle and then subtracting it with the area that is not eaten by the goat. But I don't know how to find this particular area. Was hoping the others can help me with this.
A goat is tethered at a point on the boundary of a circular grassy field, by a rope which is 1.5 times the length of the radius of the field. The field is surrounded by a fence which the goat cannot climb. What is the percentage of the grass in the field the goat can eat?
Let the radius of the field be r. Let the angle of ATB be 2β.
(T is the tethered point. With the rope at full stretch, the goat will be able to move in an arc from point A on the circumference to point B).