The team thinks the black bears are at the position of point F. The rangers use two-way radios to communicate with one another. The radios from the ranger station can only receive signals within a 65° angle before the signal is lost. A ranger team is located at point E while another team heads to point F to attempt to lure the bears to a more remote location. If the arc formed by ECF is 110°, can the ranger station communicate with both teams, or will they risk losing the signal?

Question

draco-dormiens · Answer

attachment

draco-dormiens · Answer

Can someone please explain this to me? I've been having a hard time with the question

mjdennis · Answer

Wow.  Let's translate it / reduce it:

mjdennis · Answer

Can the ranger station communicate with both teams, or will they risk losing the signal?
This means:  is angle EDF from the ranger station smaller than a 65° angle (then the station can communicate with D and F) or is it larger than a 65° angle (lose the signal)

So, if arc ECF is 110°, can you find angle EDF?

draco-dormiens · Answer

Would it be half of arc ECF?

mjdennis · Answer

|dw:1465990011074:dw|

mjdennis · Answer

I always have to look that up.  Do you already know the theorem for tanget lines?

draco-dormiens · Answer

I know the secant-tangent theorem, and and the exterior angle theorem

draco-dormiens · Answer

Wait, I think I just figured it , if I use the exterior angle theorem; I'd subtract 250 (the measure of  EBF) from 110 (measure of ECF) and I'd get 140, and half of the is 70 which means that angle EDF is 70 degrees!

mjdennis · Answer

https://www.sophia.org/tutorials/arc-measures-intersecting-outside-the-circle It turns out that it's not as simple as half the arc. (It never is the simple answer.) So, when two lines intersect outside the circle, they intersect _two_ arcs. The angle is one-half the difference between the two arcs $$m <\theta = \frac{ 1 }{ 2 }(arc2-arc1)$$ |dw:1465990642481:dw|

mjdennis · Answer

Good work, got there before I did!
and is 70 too big?  The radio can only "see" an agle up to 65, and is "blind" outside that 65 it is pointing at

draco-dormiens · Answer

Thanks for your help! Do you think you could help me with the next part of the question as well?

draco-dormiens · Answer

What description can be given to the line that connects the ranger station with either point E or point F and how do you know? You must show all work and steps to receive credit.

bigbosssaint21 · Answer

https://prezi.com/vbfyfvnv5fye/0903-module-nine-quiz/