(ii) Use your answer from part (d)(i) to find the arca of a sector of a circle of radius 7.5 cm and angle 420, giving your answer correct to two significant figures. [3] 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. Gordon likes to take his dog for a walk on the beach each morning. The beach near his home is quite large , so he can park his car on it. He has a routine that he likes to stick to. Gordon parks his car at a point ( that is 340 west of south of a point L where the lifeguard sits . He then walks in a straight line from his car to L. Next , he changes direction and walks due south along the shoreline in a straight line for 1200 metres until he reaches a large rock R, where he turns again and heads straight back to his car, which is 740 metres from the large rock. (You may assume that the beach is flat and all distances are measured in a straight line.) (a) Sketch a diagram of the situation, showing the points C for the position of Gordon's car, I for the position of the lifeguard , and R for the position of the rock . Mark in the angle and the lengths that you are given. Join the three points with line segments to make the triangle CLR, given that the angle at C is an acute angle . [2] (b) Gordon would like to calculate the distance between his car and the lifeguard . He realises that in triangle CLR 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 Gordon , why this situation is not quite so straightforward [1] (c) (i) Use the Sine Rule to find the angle at C. 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 Gordon's car and the lifeguard . Give your answer correct to two significant figures. [3] page 8 of 11