In a circle with area of 120 to 124 sq inches…

In a circle with area of 120 to 124 sq inches, the area of the sector formed by an angle is between 20 and 21 sq inches. What is one possible integer value of the angle?

I came up with a low value of 60 (if area of circle is on the lowest end, 120 sq inches, and area of the sector is also on the low end, 20 inches). If both those areas are on the highest end, then I came up with 60 again. But answer is supposed to be 59 ≤ x ≤ 63. Does this make sense, and if so, can you explain it?

In a circle with center O, the length of radius OB is 5. If the length of chord CD is 8, and if line CD perpendicular to line OB, then sin angle OCD =

Start by drawing it! Note that OC = 5 and OD = 5 because both of those are also radii. Note also that because chord CD is perpendicular to OB, it’s bisected by OB. In other words, it’s split into 2 segments each measuring 4.   Things are really coming together! Because we know our Pythagorean (more…)