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Question 5 - 20 marks Throughout this question, take care to explain your reasoning mmfully. You should round your answers, where necessary, to two signicant gures. Finn is looking into the position and range of 4G mobile towers in his local area. Finn learns that the range of the 4G mobile towers is 50km, where there are no obstructions. (a) (b) (C) Calculate what area is within the range of a 4G mobile tower where there are no obstructions. Finnlooksatamapof4Gmobiletowersinhisarea. Thereisoneat Stormer Hill and another at Blackstone Edge. The top of these towers have heights of 251 m and 4?3m respectively. Let point A be the top of the tower at Stem Hill, point B be the point vertically beneath Blackstone Edge tower and on a level with the point A and let point C be the top of the tower at Blackstone Edge. A measurement of 4cm on the map represents lien on the ground. (i) The horizontal distance between the two locations on the map is 6.5 cm. What is the actual horizontal distance between the masts (the length AB)? (ii) What is the reduction stale factor? Give your answer in standard form. (iii) What is the actual distance between the tops of the two toners, the length AC? (iv) Calculate 40.43. the angle which is the line of sight from the top of the meat at Stunner Hill to the top of the mast at Blackstone Edge. A third tower is located at low House Moor. Let DEF represent the points on the map for Stunner Hill, Blackstone Edge and Low House Moor respectively. On the map, DE = 6.5m, and EF = 5.3crn and ZDEF = 107. (i) Is [DEF on the map greater than, less than, or the same as the angle between the horizontal line between Stunner Hill and Bladrstone Edge and the horizontal line between Blackstone Edge and low House Moor in real life. Explain your answer. (ii) Find the length DF. (iii) Find the AEFD. (iv) Find the area of triangle DEF. [21 Ill [11 l2] l2] [1] I41 [3]