This question is based on your work on MU123 up to and including Unit 12. You should use trigonometry, not scale drawings, to find your answers. In an archaeological expedition, Stephanie is studying the layout of an ancient city. She has found three points of interest and straight roads joining these, forming a triangle. One road runs east-west and has a temple at one end, at point T, and a marketplace at point M, 300 metres due west of the temple. Standing at the marketplace, looking westwards (with her back to the temple), Stephanie can see a castle, C, towards the northwest. Stephanie has to turn 60 to face the castle. There is a road MC joining the marketplace and the castle which is 450 metres long. A third road, CT, runs from the castle to the temple. You may assume that the terrain is flat and all roads are along straight lines. (a) Draw a sketch, including the triangle CMT, marking the angle and the lengths (in metres) that you are given. [2] (b) (i) Find the internal angle CMT. [1] (ii) Find the distance between the castle and the temple, that is, the length of the side CT