In triangle ABC, a=5, M<B=92°, c=3.Find b.

Lennie Carroll 2020-12-17 Answered

In triangle ABC, a=5, \(\displaystyle{M}{<}{B}={92}°\), c=3. Find b.

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Expert Answer

Latisha Oneil
Answered 2020-12-18 Author has 23820 answers
The given case is SAS (two sides and included angle) so use the Law of Cosines:
\(\displaystyle{b}^{{2}}={a}^{{2}}+{c}^{{2}}-{2}{a}{c}{\cos{{B}}}\)
\(\displaystyle{b}^{{2}}={5}^{{2}}+{3}^{{2}}-{2}{\left({5}\right)}{\left({3}\right)}{\cos{{92}}}°\)
\(\displaystyle{b}^{{2}}={34}-{30}{\cos{{92}}}°\)
\(\displaystyle{b}=\sqrt{{{34}-{30}{\cos{{92}}}°}}\)
b ~ 5.92
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