Question 5 - 20 marks Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. 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 50 km, where there are no obstructions. (a) Calculate what area is within the range of a 4G mobile tower where there are no obstructions. [2] (b) Finn looks at a map of 4G mobile towers in his area. There is one at Stormer Hill and another at Blackstone Edge. The top of these towers have heights of 251 m and 473m respectively. Let point A be the top of the tower at Stormer 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 4 cm on the map represents 1 km 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)? [1] (ii) What is the reduction scale factor? Give your answer in standard form. [1] (iii) What is the actual distance between the tops of the two towers, the length AC? (2] (iv) Calculate ZCAB, the angle which is the line of sight from the top of the mast at Stormer Hill to the top of the mast at Blackstone Edge. [2] (c) A third tower is located at Low House Moor. Let DEF represent the points on the map for Stormer Hill, Blackstone Edge and Low House Moor respectively. On the map, DE = 6.5 cm, and EF = 5.3 cm and ZDEF - 1070. (i) Is ZDEF on the map greater than, less than, or the same as the angle between the horizontal line between Stormer Hill and Blackstone Edge and the horizontal line between Blackstone Edge and Low House Moor in real life. Explain your answer. (ii) Find the length DF. [4] (iii) Find the ZEFD. (iv) Find the area of triangle DEF. [3]