Triangle ASC is a right-angled triangle. We have that cos 37 = adj hyp = 2 80 SA , so SA = 2 80 cos 37 = 2 236 . . . , and so the length of SA is 2 24 m (to 2 d.p.). 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 AB2 = SA2 + SB2 - 2 SA SB cos S AB2 = 2 242 + 2 242 - 2 2 24 2 24 cos 74 AB2 = 7 269 . . . AB = p 7 269 . . . AB = 2 696 . . . . So the length of AB is 2 70 m (to 2 d.p.). Therefore the sprinkler is guaranteed to cover a length of 2 70 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. [1]

(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. [4]

(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