Question 5 - 10 marks 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. A ship leaves a port P and sails in a direction 310 east of south to reach a port Q. It then changes direction and sails a distance of 62 km to port R which is situated 80 km directly south of port P. (You may assume that all distances are flat and are measured in a straight line.) (a) Sketch a diagram of the situation, showing the points P for the first port, Q for the second port, and R for the third port. Mark in the angle and the lengths that you are given. Join the three points with line segments to make the triangle PQR, given that the angle at Q is an acute angle. [2] (b) The ship's captain would like to calculate the distance between port P and port Q. He realises that in triangle PQR he has two side lengths and an angle. He mistakenly concludes that he can solve his problem with a single direct application of the Cosine Rule, like in Example 9 in Subsection 2.2 of Unit 12. Explain, as if directly to the captain, why this situation is not quite so straightforward. [1] (c) (i) Use the Sine Rule to find the angle at Q. Give your answer correct to the nearest degree. [3] (ii) Use your answer to part (c) (i) to find the angle at R. Give your answer correct to the nearest degree. [1] (iii) Find the distance between port P and port Q. Give your answer correct to two significant figures. [3]