Notes: `A = 24.3^@, C = 54.6^@, c = 2.68` Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

Monday, 25 November 2013

$\displaystyle{A}={{24.3}}^{\circ},{C}={{54.6}}^{\circ},{c}={2.68}$ Use the law of sines to solve the triangle. (Find missing sides/angles) Round answers to 2 decimal places.

Given: $\displaystyle{A}={{24.3}}^{\circ},{C}={{54.6}}^{\circ},{c}={2.68}$

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

$\displaystyle{B}={180}-{24.3}-{54.6}={{101.1}}^{\circ}$

$\displaystyle\frac{{a}}{{\sin{{\left({24.3}\right)}}}}=\frac{{b}}{{\sin{{\left({101.1}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle\frac{{a}}{{\sin{{\left({24.3}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{a}=\frac{{{2.68}{\sin{{\left({24.3}\right)}}}}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{a}={1.35}$

$\displaystyle\frac{{b}}{{\sin{{\left({101.1}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{b}=\frac{{{2.68}{\sin{{\left({101.1}\right)}}}}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{b}={3.23}$

Given: $\displaystyle{A}={{24.3}}^{\circ},{C}={{54.6}}^{\circ},{c}={2.68}$

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

$\displaystyle{B}={180}-{24.3}-{54.6}={{101.1}}^{\circ}$

$\displaystyle\frac{{a}}{{\sin{{\left({24.3}\right)}}}}=\frac{{b}}{{\sin{{\left({101.1}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle\frac{{a}}{{\sin{{\left({24.3}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{a}=\frac{{{2.68}{\sin{{\left({24.3}\right)}}}}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{a}={1.35}$

$\displaystyle\frac{{b}}{{\sin{{\left({101.1}\right)}}}}=\frac{{2.68}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{b}=\frac{{{2.68}{\sin{{\left({101.1}\right)}}}}}{{\sin{{\left({54.6}\right)}}}}$

$\displaystyle{b}={3.23}$

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