Question

A typical television newscast has three cameras. The center camera directly faces the news anchors desk. The other two cameras are both angled 45 degrees away from the center camera. Suppose each camera has a field of 60 degrees. What is the total angle covered by the three cameras?

Answer 1

150 degrees. Let's assume the center camera is pointed to at an angle of 0 degrees. Since it has a coverage of 60 degrees, then it will cover the angles from -30 to +30 degrees. Now we'll continue to use the +/- 30 degree coverage for the other two cameras. The second camera is aimed at 45 degrees, so it's range of coverage is 15 degrees to 75 degrees (45 +/- 30). Notice that the range from 15 degrees to 30 degrees is covered by 2 cameras. Now the 3rd camera is pointed at -45 degrees, so its coverage is from -15 degrees to -75 degrees. It also has an overlap with the 1st camera from -15 to -30 degrees. The total coverage of all three cameras ranges from -75 degrees to 75 degrees. That means that an arc of 150 degrees in total is covered by all three cameras.