mu123 Maths

The student's incorrect attempt Triangle ASC is a right-anGled triangle. We have that cos 37' = adj 2 .80 hyp SA . SO SA = 2 . 80 x cos 370 = 2. 236 .... and so the length of SA is 2. 24+m (to 2 dp.) Using the Cosine Rule in triangle ASB, and the fact that the length of SA is the same as the length of SB, we have that AB 2 = SA2 + SB2 - 2 x SAX SB X COSS AB 2 = 2. 242 + 2. 242 - 2 x2. 24 x 2. 24 x COs 740 AB2 = 1. 269 ... AB = V1. 269 ... AB = 2. 696.... So the length of AB is 2. 10 m ( to 2 dp. ). Therefore the sprinkler is Guaranteed to cover a length of 2:10 m (to 2 d.p. ).(a) Look at the student's answer for the length SA. Using what you know about right-angled triangles, and without performing any further calculations, explain how you know that this calculated length must be wrong. (b) There are two places in the student's attempt where a mistake has been made. Identify these mistakes, and explain, as if directly to the student, why, for each mistake, their working is incorrect. (c) Do you think the student's approach to solving the problem is the most efficient method? Give a reason for your answer. (d) Write out your own solution to the problem, explaining your working