Angles A, B and C of a triangle ABC are in A.P. With the usual notations if and then angle A is equal to

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Angles A, B and C of a triangle ABC are in A.P. With the usual
notations if
$\frac{b}{c} = \frac{\sqrt{3}}{\sqrt{2}}$ and $\angle C = \frac{\pi}{4}$
then angle A is equal to

Show answer and solution

\frac{b}{c} = \frac{\sqrt{3}}{\sqrt{2}} \Rightarrow \frac{b}{\sqrt{3}} = \frac{c}{\sqrt{2}} \Rightarrow \frac{b}{\frac{\sqrt{3}}{2}} = \frac{c}{\frac{1}{\sqrt{2}}}

But we know that

\frac{b}{sinB} = \frac{c}{sinC} = \frac{a}{sinA}

\therefore

B = \frac{\pi}{3};C = \frac{\pi}{4} \Rightarrow A = \frac{5\pi}{12}

Source: Grass-G / M-24 Mathematics Paper 31 Dec.docx

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