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

Question
In triangle ABC, a=5, $$\displaystyle{M}{<}{B}={92}°$$</span>, c=3. Find b.

2020-12-18
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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