The sides of triangle have lengths 7,5.1, and 6.2. What

Rena Giron 2021-11-22 Answered
The sides of triangle have lengths 7,5.1, and 6.2. What kind of triangle is it?
Find f.
image
Write your answer in simplest radical form.

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Expert Answer

Roger Noah
Answered 2021-11-23 Author has 8396 answers
a) Given sides of triangle have lengths 7,5.1, and 6.2
Since all the sides are different.
image
Let \(\displaystyle{c}={7}\) (largest side)
\(\displaystyle{a}={5.1}\) and \(\displaystyle{b}={6.2}\)
\(\displaystyle{c}^{{2}}={7}^{{2}}={49}{<}{\left({5.1}\right)}^{{2}}+{\left({6.2}\right)}^{{2}}={a}^{{2}}+{b}^{{2}}\)</span>
\(\displaystyle{c}^{{2}}{<}{a}^{{2}}+{b}^{{2}}\)</span>
if \(\displaystyle{c}^{{2}}{<}{a}^{{2}}+{b}^{{2}}\)</span>, then the triangle is an acute triangle
Acute b) Since \(\displaystyle{m}\angle{A}{C}{B}={m}\angle{A}{B}{C}={4}{s}\)
image
\(\displaystyle\Rightarrow{A}{B}={A}{C}={f}\)
\(\displaystyle{A}{B}={f}\)
\(\displaystyle{9}{n}\triangle{A}{B}{C},{A}{C}^{{2}}={A}{B}^{{2}}+{A}{C}^{{2}}\)
\(\displaystyle={f}^{{2}}+{f}^{{2}}={2}{f}^{{2}}\)
\(\displaystyle\Rightarrow{4}={2}{f}^{{2}}\Rightarrow{f}^{{2}}={2}\)
\(\displaystyle{f}=\sqrt{{{2}}}={1.414}\)
\(\displaystyle{f}={1.414}\)
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