Final is in a neighborhood so better not done at night.
My name is Sam Spade. You probably know about me. Detective, walking the streets. Everyone was after the black bird and then this Muggsy Muggle walked in and put a gun to me. He would have done anything to get this bird. I turned the tables on Muggsy, he’s a low life punk. I managed to get my hands on the black bird and put it away for safekeeping.
I called up my Girl Friday, Trudy Cacher, and gave her instructions to get the black bird and bring it over. It was a bad break for her. She was followed and decided to hide the bird. She hid the bird before she was shot and she sent me a message. I’m sure the message is the location of the black falcon. Can you help me find it? This is her message:
"Standing at these coordinates, I noticed the coincidence of the school's mascot being a falcon, in fact a Black (Blach) Falcon. The school has a giant sundial formed from part of the structure. That gave me the idea for a way to hide the bird that will befuddle Muggsy. I used a small plaque here and the time of day from the sundial to hide the Black Bird. I'm sure a smart detective can do the math and solve the coordinate projection.
I noted the sun angle on the building sundial and confirmed with my watch that it was 3 pm Standard Time. First I got the nearest whole angle from the solar noon line to the 3pm line. Call it AA.
How to determine AA, Sundial Angle from Solar Noon (don't share this with Muggsy)
To compute the sundial angle for a particular time, you need the latitude and the time. The sun's hour angle moves by 15 degrees an hour starting from noon. So at 1 pm it is 15°, 2 pm 30° and 3 pm 45°. You will need the sin of the latitude. For 37° here, that is 0.6018150.
Compute sin(37°) * tan(45°). Finally, take the arctan of this value to get the angle in degrees on the sundial. Be sure your calculator is working in degrees and not radians. You only want the whole number of degrees.
If you don't have a calculator handy, there may be other "source" tools lurking that you can find to help you without resorting to calculation.
I then noted the Troop number on the nearby sign. Call the first digit of the troop number N.
Angle to project = NAA degrees +1
Distance in feet = 3328
At the projected location, you can find the Black Bird. Don't let Muggsy see you though. Be very stealthy. Detailed hint is in Certitude along with exact coordinates since your calculation may vary slightly.
You can validate your puzzle solution with certitude.