Notes: `B = 28^@, C = 104^@, a = 3 5/8` Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

Sunday, 12 November 2017

$\displaystyle{B}={{28}}^{\circ},{C}={{104}}^{\circ},{a}={3}\frac{{5}}{{8}}$ Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

Given: $\displaystyle{B}={{28}}^{\circ},{C}={{104}}^{\circ},{a}={3.625}$

The Law of Sines: $\displaystyle\frac{{a}}{{\sin{{\left({A}\right)}}}}=\frac{{b}}{{\sin{{\left({B}\right)}}}}=\frac{{c}}{{\sin{{\left({C}\right)}}}}$

$\displaystyle{A}={180}-{28}-{104}={{48}}^{\circ}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{b}}{{\sin{{\left({28}\right)}}}}=\frac{{c}}{{\sin{{\left({104}\right)}}}}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{b}}{{\sin{{\left({28}\right)}}}}$

$\displaystyle{b}=\frac{{{3.625}{\sin{{\left({28}\right)}}}}}{{\sin{{\left({48}\right)}}}}$

$\displaystyle{b}={2.29}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{c}}{{\sin{{\left({104}\right)}}}}$

$\displaystyle{c}=\frac{{{3.625}{\sin{{\left({104}\right)}}}}}{{\sin{{\left({48}\right)}}}}$

$\displaystyle{c}={4.73}$

Given: $\displaystyle{B}={{28}}^{\circ},{C}={{104}}^{\circ},{a}={3.625}$

The Law of Sines: $\displaystyle\frac{{a}}{{\sin{{\left({A}\right)}}}}=\frac{{b}}{{\sin{{\left({B}\right)}}}}=\frac{{c}}{{\sin{{\left({C}\right)}}}}$

$\displaystyle{A}={180}-{28}-{104}={{48}}^{\circ}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{b}}{{\sin{{\left({28}\right)}}}}=\frac{{c}}{{\sin{{\left({104}\right)}}}}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{b}}{{\sin{{\left({28}\right)}}}}$

$\displaystyle{b}=\frac{{{3.625}{\sin{{\left({28}\right)}}}}}{{\sin{{\left({48}\right)}}}}$

$\displaystyle{b}={2.29}$

$\displaystyle\frac{{3.625}}{{\sin{{\left({48}\right)}}}}=\frac{{c}}{{\sin{{\left({104}\right)}}}}$

$\displaystyle{c}=\frac{{{3.625}{\sin{{\left({104}\right)}}}}}{{\sin{{\left({48}\right)}}}}$

$\displaystyle{c}={4.73}$

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