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C.
Solve for the missing parts of ∆ABC on the right.

Given: two sides and an angle opposite one of these sides
a= 10
c=19
<C=120°



c=19
A
b
c
120°
a=10
B​


Sagot :

[tex]\Large\color{blue}{{\underline{\mathfrak {{꧁☆☬ Answer ☬☆꧂ }}}}}[/tex]

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[tex]\small\color{black}{{\underline{\bold{Using \:the \: law \: of \:sine}}}}[/tex]

[tex]\small\color{black}{{\underline{\bold{\frac{10}{ \sin(A) } = \frac{19}{ \sin(120) } } }}} \\ \\ = \sin {}^{ - 1} (A) = \frac{10 \sin(120) }{19} \\ =\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: A=27.1\:\:\:\: }}}}[/tex]

[tex]\small\color{black}{{\underline{\bold{{27.1°+B+120°=180° } } }}}\\= < B=147.1-180°\\ = \small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: B=32.9\:\:\:\: }}}}[/tex]

[tex]\small\color{black}{{\underline{\bold{\frac{10}{\sin(27.1) } = \frac{b}{ \sin(32.9) }}}}} \\ \\ b = \frac{10 \sin(32.9) }{ \sin(27.1) } \\ =\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: b=11.9\:\:\:\: }}}}[/tex]

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