A man hiking through the Ocala National Forest became disoriented after the compass app on his cell phone stopped working. He called local authorities on a non-emergency line to report his situation. Through a series of three separate phone calls, the search-and-rescue team has used cell phone towers to narrow the area to search for the lost hiker. The three coordinates are located as follows: A (–6, –1), B (2, 6), and C (4, –5). The search-and-rescue team has concluded that the hiker is somewhere within the area bound by the inscribed circle and circumscribed circle formed using the three
(question continued)---coordinates that form the triangle. Use the three coordinates and graph paper to construct the inscribed circle and circumscribed circle to help the team locate the missing man. Explain using words how you constructed the circumscribed circle and inscribed circle and what steps were involved in the process.
Below is a diagram of a previous search the team performed last summer while searching for a pack of black bears that were disturbing campsites. The team's goal was to find and relocate the bears to a more remote part of the forest. A diagram of a circle is shown with the center of the circle labeled Lookout Tower. Three collinear points are labeled campsite 1, campsite 2, and ranger station. Lookout Tower is labeled point A, Campsite 2 is labeled point B, campsite 1 is labeled point C, and the ranger station is labeled point D. Two additional points E and F are located on the circle. Campsite 1 and campsite 2 are located on the circle and the ranger station is located outside the circle. Answer the following questions using the diagram. Question 1: Campsite #1, lookout tower, and campsite #2, form a central angle within the circle. If the angle formed is 120°, describe the relationship between the angle and the arc it intercepts. You must show all work to receive credit. Question 2: An inscribed angle is formed by lookout tower, campsite #1, and campsite #2. If the angle formed is 30 degrees, describe the relationship between the angle and the arc it intercepts along the circle. You must show all work to receive credit. Question 3: 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? 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?
Please just post one question at a time thank you!!! :)
Join our real-time social learning platform and learn together with your friends!