[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{꧁☆☬ Answer ☬☆꧂}}}}}}[/tex]
[tex]______________________________[/tex]
[tex]\small\color{black}{{\underline{\bold{The\: Law\: of \:cosines}}}}[/tex]
[tex]\small\color{black}{{\underline{\bold{Example:}}}}[/tex]
[tex]b=14,c,=16,A=128°[/tex]
[tex]\small\color{black}{{\underline{\bold{{a}^{2} \sqrt{ {14}^{2} +{16}^{2} - 2(14)(16) \cos(128°)}}}}} \\ = \small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: a=26.9\:\:\:\: }}}}[/tex]
[tex]\small\color{black}{{\underline{\bold{\cos ^{ - 1} = \frac{{26.9}^{2} +{ 16}^{2} - {14}^{2} }{2(26.9)(16)}}}}} \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: B=88.0\:\:\:\: }}}}[/tex]
[tex] \cos^{ - 1} = \frac{26.9 + 14 - 16}{2(26.9)(14)} \\ \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: C=88.1\:\:\:\: }}}}[/tex]
[tex]______________________________[/tex]
[tex]\small\color{black}{{\underline{\bold{ The \:law \:of \:sines} }}}[/tex]
[tex]\small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: Example:\:\:\:\: }}}}[/tex]
a=4,c=12,C=120°
[tex]\small\color{black}{{\underline{\bold{\frac{4}{ \sin(A) } = \frac{12}{ \sin(120) } } } } } \\ = \sin { }^{ - 1} = \frac{4 \sin(120) }{12} \\ = \small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\:A=16.7\:\:\:\: }}}}[/tex]
[tex]16.7°+B+120°=180°\\=B=120°+16.7=136.7\\=B=136.7°-180°\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\:B=43.3\:\:\:\: }}}}[/tex]
[tex]\small\color{black}{{\underline{\bold{ \frac{4}{ \sin(16.7) } = \frac{b}{ \sin(43.3) } } } } } \\ b = \frac{4 \sin(43.3) }{ \sin(16.7) } \\ = \small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\:b=9.5\:\:\:\: }}}}[/tex]
[tex]______________________________[/tex]
[tex]\Large\color{red}{{\underline{\mathfrak {{@Carry\:on\: learning }}}}}[/tex]
