Hey,
I have a problem that I have been working on for a while now, exhausting many algebraic and trig. approaches. Here it is:
Points A, B, C, and D lie equally spaced along a line in the order given wth AB = BC = CD = 1. A point P is located such that sin(angleAPC) = 3/5 and sin(angleBPD) = 4/5. Determine sin((2)angleBPC).
The hint given was "Extended Law of Sines", which of course is a/sin a = 2R. I see how this provides calculations for the radii of the circumscribed circles of triangles APC and BPD, but can't figure out how this helps with finding 2sinBPC. Also, I know that angles APC and BPD add up to 90 degrees. Maybe I'm overlooking something really obvious. Thanks for any tips!
I have a problem that I have been working on for a while now, exhausting many algebraic and trig. approaches. Here it is:
Points A, B, C, and D lie equally spaced along a line in the order given wth AB = BC = CD = 1. A point P is located such that sin(angleAPC) = 3/5 and sin(angleBPD) = 4/5. Determine sin((2)angleBPC).
The hint given was "Extended Law of Sines", which of course is a/sin a = 2R. I see how this provides calculations for the radii of the circumscribed circles of triangles APC and BPD, but can't figure out how this helps with finding 2sinBPC. Also, I know that angles APC and BPD add up to 90 degrees. Maybe I'm overlooking something really obvious. Thanks for any tips!