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Please give an answer with detailed steps and explanations.

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Best answer

\(\delta\) = 30°

i = 90°

i = \(\frac{\delta+A}2\)

90 = \(\frac{30+A}2\)

180 = 30 + A

a = 150°

\(\mu\) = \(\cfrac{sin(\frac{A+S}2)}{sin(\frac A2)}\) 

\(\mu\)  = \(\cfrac{sin(\frac{150+30}2)}{sin(75^{\circ})}\)

\(\mu\) = \(\frac{sin(90^{\circ})}{sin(45^{\circ}+30^{\circ})}\)

\(\mu\) = \(\frac1{sin45^{\circ}cos30^\circ+cos45^\circ.sin30^\circ}\)

\(\mu\)  = \(\cfrac1{\frac1{\sqrt2}\times\frac{\sqrt3}2+\frac1{\sqrt 2}\times\frac12}\)

 = \(\cfrac{1}{\frac{\sqrt3}{2\sqrt2}+\frac1{2\sqrt2}}\) = \(\cfrac1{\frac{\sqrt3+1}{2\sqrt2}}\) = \(\frac{2\sqrt2}{\sqrt3+1}\)

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