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Use the converse of the Pythagorean theorem to decide if the triangles are right, acute or obtuse. Then classify them.

(show work) pls help!!!!!! i’m confused

Use the converse of the Pythagorean theorem to decide if the triangles are right, acute-example-1

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Answer:


\mathrm{a\ right\ triangle}

Explanation:


\mathrm{The\ converse\ of\ pythagoras\ theorem\ states\ that\ if\ }c^2=a^2+b^2\ \mathrm{then\ it\ is}\\\mathrm{a\ right\ angled\ triangle.\ We\ can\ therefore\ use\ the\ converse\ to\ check\ if\ a}\\\mathrm{triangle\ is\ right\ angled\ or\ not.}\\\mathrm{Here\ in\ the\ question\ we\ are\ given\ a\ triangle\ with\ 3\ sides.\ Let's\ take\ the }\\\mathrm{longest\ one\ has\ hypotenuse.\ So,\ let\ c=√(50),\ a=5\ and\ b=5.}\\


\mathrm{Finally,\ we\ want\ to\ test\ whether\ the\ given\ triangle\ is\ right\ angled\ or\ not\ }\\\mathrm{i.e.\ is\ }c^2=a^2+b^2?\\c^2=√(50)^2=50.\\a^2+b^2=5^2+5^2=25+25=50\\\mathrm{Here,\ the\ pythagoras\ theorem\ }c^2=a^2+b^2\ \mathrm{is\ satisfied\ so\ the\ triangle\ is}\\\mathrm{right\ angled\ triangle.}

I hope this clarifies your doubt!

User Sebastian Siemens
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