Question.6

Remember that you need to explain your reasoning and communicate your ideas clearly and explain your mathematics in the context of the question.

In this question, you are asked to comment on a student's incorrect attempt at answering the question detailed below. (a) Write out your own solution to the question, explaining your working. (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. The Question D 18.4 cm 15.2 cm C B Triangle ABC is a right-angled triangle. The length of side BC is 15.2 cm. ZCAB = 40 and ZBCA =909. D is a point on side CA, and BD has length 18.4 cm. (i) Find ZCDB and hence ZADB, giving your answers to two significant figures. (ii) Find the length of DC, giving your answer to two significant figures. (iii) Use your answer to part (i) to find the length of AB, giving your answer to two significant figures.The student's incorrect attempt (i) In triangle DBC, the known sides are the hypotenuse and the side opposite to ZCDB, so the ratio needed is sine. sin (ZCDB) = 15.2 18.4 ZCDB = Sin" ( 15.2 18.4 = 55.6 ... So ZCDB is 560 (to 2 s. f.) ACD is a straight angle so is 180 There fore ZADE = 180' - 55.6...' = 124.3..." So ZADE is 1200 (to 2 s.f.)(Li) Triangle BCD is a right-angled triangle so using Pythagoras' Theorem DB = CB3+ DC2 DO? = DE - CB2 DC = DB - CE DC = 18.4 - 15.2 = 3.2 The Length of DC is 3.2 cm (to 2 s. f.) (ill) using the sine rule in triangle ABD AB DB Sin (ZADE) Sin (ZDAB) AB 18.4 sin (120') sin (409) AB = 18.4 x sin (120') sin (409) = 24.7 ... The Length of AB is 25 cm (to 2 s.f.)