Given a triangle with legs a and b and hypotenuse c, find the length of side b if c=2b, a=\sqrt[2]{3}

Question

Given a triangle with legs a and b and hypotenuse c, find the length of side b if c=2b, a=
`\sqrt[2]{3}`

Answer 1

Answer:2

Explanation:

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Answer 2

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - a^2)=b \qquad \begin{cases} c=\stackrel{hypotenuse}{2}\\ a=\stackrel{adjacent}{\sqrt[2]{3}}\\ \qquad √(3)\\ b=opposite\\ \end{cases} \\\\\\ 2^2=(√(3))^2+b^2\implies 4=√(3^2)+b^2\implies 4 = 3 +b^2 \\\\\\ 1=b^2\implies √(1)=b\implies 1=b`