The student's incorrect attemptwe first calculate the angle at A, using the fact that all threeangles in a triangle add up to 180°. We haveA = 180 - (90 + 36) = 54,so the anGle at A is 54°.Using the Sine Rule in triangle ABP, we haveaPsin Asin?'SOa =x sinAsinpI08x sin 54°sin 120= 91.81....So the lenath of BP is 92 inches (to the nearest inch).The length of BP is the same as the length of AP, and triangleACP is right-angled, so we haveadj _ CP92hypcos 36° =%3DSO92= 13.1....cos 36°Therefore to the nearest inch, the projector should Be placedt inches away from the centre of the viewinG area.(a) Look at the student's answer for the length CP. Using what you knowabout right-angled triangles, and without performing any furthercalculations, explain how you know that this calculated length must bewrong.(b) There are two places in the student's attempt where a mistake has beenmade. Identify these mistakes, and explain, as if directly to the student,why, for each mistake, their working is incorrect.(c) Do you think that the student's approach to solving the problem is themost efficient method? Give a reason for your answer.(d) Write out your own solution to the problem, explaining your working. The QuestionRonan is building an extension to his house to facilitate a social spaceand games room. One of his passions is watching sport on a big screen,so he has purchased a wide-lens home cinema projector that he canconnect to his laptop, instead of buying a large-screen TV. Having readthe manufacturer's guide extensively, and researched his options on theinternet for optimising picture quality, he decides that he would like tohave a viewing area equivalent to having a 120-inch TV mounted on thewall. This means that the width of the viewing area will be 108 inches.The projector has a wide lens that covers an angle of 72°. He needs toposition the projector centrally with respect to the viewing area, on astand that you may assume is at the correct height for optimum picturequality.Ronan sketches the situation in Figure 7, where all lengths are measuredin inches. The point P represents the projector's position on the stand.Points A and B are the furthest reaches of the viewing area (the width).The point C is the centre point of the screen's width, directly in front ofthe projector. The length of PA is equal to the length of PB. AngleAPB is 72°, so angle APC is 36°.108AB36PFigure 7Assuming that all aspects of picture quality are satisfactory, how far fromcentre point C should the projector be placed in order to fill the fullscreen width of 108 inches?

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This is a problem related to trigonometry parts. Based on the general formula we will calculate the…

Figure 7 Assuming that all aspects of picture quality are satisfactory, how far from centre point C should the projector be placed in order to fill the full screen width of 108 inches?