MHB Trigonometry: Right-angled triangle

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The discussion focuses on a student's solution involving a right-angled triangle, highlighting errors in their algebra and trigonometric calculations. Part (i) of the student's response is correct, but part (ii) contains a mistake in calculating the length of DC, as the relationship DC^2 = DB^2 - CB^2 does not simplify to DC = DB - CB. For part (iii), while the trigonometric approach is valid, using 120 degrees for angle ADB is criticized for potentially causing rounding errors. Instead, applying the equation sin(40) = BC/AB is recommended to avoid inaccuracies in determining the length of AB. Overall, the discussion emphasizes the importance of accurate calculations in trigonometry.
Brian Bart
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part (i) of the student's response is correct.

part (ii) has an algebra error in determining the length of DC

if $DC^2 = DB^2 - CB^2$, then $DC \ne DB - CB$

the trig for part (iii) is correct ... can't say I agree with using 120 degrees for angle ADB since it induces rounding error in determining the length of AB.

Using the equation $\sin(40) = \dfrac{BC}{AB} \implies AB = \dfrac{BC}{\sin(40)}$ will not induce that error.
 
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Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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