# A motion detector can detect motion up to 25 m away through an angle of 75 degrees. A. What area can the motion dectector monitor? B. For r=25 m what angle is required to monitor 50% more area?C. for 75 degrees what range is required for the detector to monitor 50% more area?

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A motion detector can detect motion up to 25 m away through an angle of 75 degrees.

A. What area can the motion dectector monitor?

B. For r=25 m what angle is required to monitor 50% more area?

C. for 75 degrees what range is required for the detector to monitor 50% more area?

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Step 1

According to the given information, a motion detector can detect motion upto 25m through an angle of 75 degrees.

In part (A) it is required to calculate the area of the motion detector monitor that can be calculated as:

Step 2

For part (B) it is required to calculate the angle for r = 25 when it monitors 50% more area.

So, 50% more area is:

Step 3

Now, using this area cal...

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