Question 326101
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Use Pythagoras.  Let *[tex \Large b] represent the measure of side b.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (3x)^2\ =\ x^2\ +\ b^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9x^2\ -\ x^2\ =\ b^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8x^2\ =\ b^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ 2x\sqrt{2}]


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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(A)\ =\ \frac{x}{3x}\ =\ \frac{1}{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(B)\ =\ \frac{2x\sqrt{2}}{3x}\ =\ \frac{2\sqrt{2}}{3}]


Hence the exact answers are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \sin^{-1}\left(\frac{1}{3}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ B\ =\ \sin^{-1}\left(\frac{2\sqrt{2}}{3}\right)]


Start punching the calculator if you need numeric approximations.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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