Two students are solving a physics problem and set up the triangle below. P 2.2 m 26° 4.6 m The students discuss how to find the length of the side labeled p. Student 1: We can use Pythagoras. I think it's p-squared plus 2.2-squared equals 4.6. Student 2: Or we could use a trig. function. Sine of 26 equals 2.2 over p. Then solve for p. Which student do you think is correct? Both Student 1 and Student 2 are incorrect. Student 2 is correct; Student 1 isn't. Both Student 1 and Student 2 are correct. Student 1 is correct; Student 2 isn't
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We are given a triangle with sides 2.2m and 4.6m, and an angle of 26°. We need to find the length of the side labeled p. Show more…
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The student's incorrect attempt We first calculate the angle at A, using the fact that all three angles in triangle ACF add up to 180°. So we have A = 180 - (90 + 26) = 64. So the angle A is 64°. Using the Sine Rule in triangle ABF, we have a / sin A = f / sin F so a = f / sin F × sin A = 5 / sin 52° × sin 64° = 5.702 ... So the length of BF is 5.7 m (to 1 d.p.). The length of BF is the same as the length of AF, and triangle ACF is right-angled, so we have cos 26° = adj / hyp = CF / 5.7 , so CF = 5.7 / cos 26° = 6.341... Therefore, to 2 decimal places, the fan should be placed at least 6.34 m away from the centre of the room. (a) Look at the student's answers for the lengths BF and CF. Using what you know about right-angled triangles, and without performing any further calculations, explain how you know that at least one of these calculated lengths 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.
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