Question

(please help me by explaing)

After dinner, your aunt serves slices of apple pie. Would you rather have a slice with a central angle equal to


(a) one radian


(b) 45 degrees?


You must choose (a) or (b) and explain why you chose one over the other.

Answer 1

Option A is the better option.

The better option would be to pick the slice of pie with a central angle of 1 radian as it is a bigger slice of pie than the 45° central angle pie.

Explanation:

The best way to pick the better/bigger option is to convert the two angular measures into the same angular units.

a) 1 radian

2π radians = 360°

1 radian = (1×360°)/2π = 57.3°

b) 45°

360° = 2π radians

45° = (45°×2π)/360 = 0.785 radian

So,

57.3° > 45°

1 radian > 0.785 radian

Hence, it is advisable to pick the slice of pie with central angle of 1 radian as it is a bigger slice of pie than the slice of pie with central angle of 45°.

Hope this Helps!!!